Odom was also able to get up from his hospital bed and sit in a chair with no apparent distress.
Kim Kardashian posted on Instagram after a visit stating: "I have faith in you. I believe in the power of prayer and positive energy! Thank you all for your prayers! Lammy- I'm so happy Kendall & I could make you smile today! God is good!"
This follows similar reports from several other outlets that Odom had opened his eyes and asked to see his kids. A source at the hospital told Entertainment Tonight that Odom opened his eyes and was somehow able to communicate 'yes' when asked if he wanted to see his children.
The 35-year-old is believed to have suffered a stroke after overdosing on drugs during a four-day $75,000 bender at Dennis Hof's Love Ranch brothel in Pahrump, Nevada.
While his family's prayers have been answered, it's still uncertain what long term damage the former LA Laker faces.
Since Odom's collapse, his prospects of recovery have looked grim according to several outlets who gave reports that he was 'in dire straights' and with just a 50/50 chance of survival.
It was previously reported that four of Odom's organs - including his kidneys - were failing and that doctors were losing hope for him the longer he was in a coma.
The good news about Odom's breakthrough comes after security footage emerged which appears to show him taking pills and drinking with a prostitute in the brothel where he was found unconscious.
The surveillance clip reportedly shows the basketball star slumped over in his seat as he is given a drink and a shot by the bikini-clad woman at the Love Ranch Vegas on Saturday - three days before he collapsed.
Odom, 35, is later apparently seen taking a pill out of a small bag and popping it into his mouth, it was reported by Radar Online.
However, it is not clear from the grainy footage what the person was taking or whether he did ingest anything.
Kris Jenner and her daughters Kim, Kourtney and Kylie were seen arriving at the hospital together on Thursday, and left a few hours later, boarding a private jet out of town.
The women looked somber for the hospital visit, wearing all black and sunglasses.
Ex-wife Khloe Kardashian refused to leave Odom's side. A report by the New York Daily News claimed that Caitlyn Jenner flew to be with Khloe, but a rep for Jenner told US Weekly those reports are false.
The Kardashian family reportedly plan to fly back to Las Vegas at the weekend to spend more time with Odom.
Posting identical statements online last night, Khloe, Kim, Kendall, Kylie and Kourtney said they had suspended all activity on their paid-for apps while they focus on his recovery.
Explaining their lack of activity to fans, they said: 'As a family we've decided to hold off on publishing content across our apps while we continue to support and pray for Lamar.
'Thank you for your kindness and understanding during this difficult time.
Lamar Odom's children, Lamar Jr and Destiny, have also spoken about their father, after Khloe reportedly paid to fly them to Las Vegas.
In a statement given to E! News, they said: 'Thanks for your outpouring of prayers and support for our dad.
'We are here with our family and friends. We appreciate everyone respecting our privacy at this time. We ask for your continued prayers.
Destiny, 17, and Lamar Jr, 13, arrived in Las Vegas Wednesday night along with their mother Liza Morales and Lamar's aunt JaNean Mercer
Since Odom was placed in a medically-induced coma on Tuesday, a Nevada brothel madam came out and told the story of how the tormented former basketball player poured his heart out to her during his stay at the ranch.
In an exclusive interview with Daily Mail Online, Love Ranch general manager TJ Moore revealed how the ailing reality star enjoyed as many as six private 'party sessions' each day with a pair of blonde hookers.
The two-time NBA champ picked Ryder Cherry and Monica Monroe from a parade-style line-up that included a transsexual escort and five other scantily-clad women - before summoning the girls to his private suite.
He also stunned staff with his bottomless appetite, gorging on KFC buckets and three T-bone steaks at a time - and by asking for private time with grandmother-of-two Moore, 52, who runs the ranch for boss Dennis Hof.
'It was surprising. I was a little nervous at first but it was clear he just wanted to talk,' TJ told Daily Mail Online. 'He's been hurt a lot, I think he doesn't know who to trust.
'I was with him for quite a while. He was mellow, melancholy almost. He gave me a kiss on the cheek, like a son would kiss a mother.'
Among the women included for Lamar to pick - reportedly at his personal request - was transsexual Love Ranch worker Madison Montag.
'In the car on the way out there [from Las Vegas] he talked about the fact that he had met Madison Montag, our transsexual prostitute, online... and he wanted to meet her,' ranch owner Dennis Hof said in an interview with Todd Shapiro and Jay Brady of Sirius XM 168's Todd Shapiro, reports Radar Online.
Hof claimed the two had met through Instagram.
Radar also reported that Odom indulged in a $5,000-a-day bender at The Spearmint Rhino in Las Vegas just a week before his binge at the Love Ranch.
A dancer at the high-end gentleman's club said the star spent five consecutive days in the VIP room and allegedly asked staff for sexual favors.
'He was spending money like crazy,' the woman said, adding that he splashed out $5,000 a day on alcohol, non-stop lap dances and VIP treatment.
'He was making all the girls drink and party with him,' she added.
The insider claims she and other girls were asked to 'entertain him' but she refused his sexual advances because she heard he was 'difficult and demanding'.
News of his time at the Love Ranch brothel comes as a new report sheds light on Odom and Khloe's tormented relationship in the weeks before his tragic overdose during the $75,000 bender.
According to Radar Online, Odom had 'pleaded' with Khloe to stop recording his phone calls for her reality show, but she reportedly ignored his requests, saying he deserved the bad press for the way he treated her during their marriage.
'Khloe would either ignore the texts and voice mail messages asking her to stop, or she would tell him, "You owe me this after you humiliated me by cheating with other women",' the source said.
This comes from an insider who told the gossip site that they believe the Kardashians 'have blood on their hands' for 'demonizing and exploiting' Odom on their show.
'Lamar had no idea that he was going to be Khloe's storyline during the past season. She is always talking about how much she loves the guy, but has no problem exploiting Lamar for her gain.
'How low can Khloe go?' the source asked. 'Lamar would call her sobbing about losing his best friend this past summer, and the first thing she thinks is to document it?'
This echoes previous statements from Hof and prostitutes at the Love Ranch who said Odom became 'irate' and inconsolable after talking to someone on the phone on Sunday, allegedly about his portrayal on the show.
While Odom and Khloe have been separated since 2013, he has still remained a central point on the family's reality show.
One plot point on a recent episode involved Kim getting mad at Khloe for 'flirting' with her ex-husband on the phone.
The two signed divorce papers in July, but their split has not been finalized, so Khloe has been by Odom's side at the hospital, making medical decisions for him while he is in a coma.
While the couple's divorce has alienated Odom from the Kardashians in recent years, news of his collapse has brought the family together again, showing their deep-seated love for the former LA Lakers player.
Meanwhile, the father of star's best friend, who died from drug use in June, said he believed the pair had a 'death wish'.
Guillermo Castillo, who lost his son Jamie Sangouthai to a flesh-eating bacteria he caught through intravenous drug use, told the New York Daily News: 'I think Lamar is done. I think most of it is because he missed my son so much.
'I think deep inside they had a death wish, or a wish to die together. It sounds very cold-blooded, but I have a hard time controlling my emotions.'
Castillo said of Lamar and Jamie's friendship: 'They were so close. They wouldn't even go to the bathroom without asking the other. They couldn't live without each other.'
Jamie was the best man at Lamar's 2009 wedding to Khloe, and also appeared on the couple's E! reality show Khloe & Lamar.
And while Castillo had nothing but kind words to say about Khloe, he did say that he warned Lamar to avoid the pitfalls of fame when the basketball star called him in June shortly after Jamie's death.
'I told him, "I'm a street kid, walk the F away from everything right now because Hollywood is going to eat you up and spit you out too." But he had money and status. Why would he listen to me?' said Castillo.
That was the last time he spoke to Lamar, saying that despite repeated attempts to reach out he never was able to get in touch because he would constantly change his phone number.
Lamar suffered tragedy yet again shortly after Jamie's death, when another friend - Bobby Heyward - died of a drug overdose.
- Daily Mail
