"We were having a chat and he got quite emotional," Jessica said.
"I said 'Do you want me to come up?' and he said 'Yes, I do. I need you Mum.'"
Parker's brave actions also sparked an outpouring of support from people moved by his story and well-wishers have raised £50,000 ($90,000) to help him turn his life around.
"He's completely overwhelmed by it all," Jessica said.
"He never envisaged that sort of money, ever."
Michael Johns, who set up the GoFundMe page, said: "Like many others I have been horrified by the news from Manchester.
"Among the sad details, one story has stood out for me and compelled me to make an effort to help one of our most vulnerable in society who showed great selflessness and courage.
"This GoFundMe campaign is for the benefit of Chris Parker [who] selflessly and heroically ran towards the blast zone to help those affected."
The rough sleeper tearfully recalled the moment a woman died in his arms and how he helped a little girl who lost her legs in the atrocity.
"Everyone was piling out, all happy and everything else. As people were coming out of the glass doors I heard a bang and within a split second I saw a white flash, then smoke and then I heard screaming," he said.
"It knocked me to the floor and then I got up and instead of running away my gut instinct was to run back and try and help.
"There was people lying on the floor everywhere.
"I saw a little girl. She had no legs. I wrapped her in one of the merchandise T-shirts and I said 'where is your Mum and Daddy?' She said 'my dad is at work, my mum is up there'."
He added: "[The woman] passed away in my arms. She was in her 60s and said she had been with her family.
"I haven't stopped crying.
"The most shocking part of it is that it was a kids' concert."
GoFundMe has confirmed it has been in contact with the page's creator about his fundraising efforts.
Parker was just one of the many heroes who shone light in Manchester's darkest hour.
