Kensington Palace has refused to comment on the matter.
Social media goes into overdrive
Royal wedding fans are glued to social media, news websites and keeping an eye on the telly as they wait to hear that the fifth-in-line to the throne has indeed proposed to his actress girlfriend.
One source has said an announcement could come today leading to feverish excitement online about a new royal wedding.
Rob Young tweeted: "Rumour has it Prince Harry and Meghan Markle's engagement will be announced at 5pm today".
Aine McManus said: "I cannot cope with being sick - convinced the only thing that will cure me is an official announcement of Prince Harry and Meghan Markle's engagement."
@MiajltF said: "We all are guessing for the announcement !! Harry and Meghan will announce it tomorrow 11am UK time!! It's still unofficial but we all are betting on it".
Katherine Findleys said: "Crosses fingers for Harry and Meghan engagement announcement. I LOVE a royal wedding".
@RoyallyPetite said: "The rumours of Prince Harry and Meghan Markle's engagement have stepped up a notch with reports that a television announcement has already been recorded".
Bookmakers stop taking bets
Bookmakers have stopped taking bets on the couple getting married and say there has been a sudden burst of wagers on a May wedding.
There has been a flurry of specific bets about the wedding taking place in April or May, just after the due date of the Duke and Duchess of Cambridge's third child.
A Betfair spokesman said: "We saw some quite interesting betting on May 2018 to be the date for the wedding.
"Originally the favourite months had been June and July but these bets were quite specific about May.
"We don't think there is anything suspicious but there had been lots of reports yesterday about the BBC being put on stand-by and also May would be the first opportunity after Kate has her baby."
Intriguingly Windsor Castle is closed on April 20 this year and its state apartments will be shut on the day before and afterwards, but the castle told MailOnline they would not comment on private events.
Westminster Abbey is the favourite on the betting markets followed by St Paul's Cathedral.
11 reasons why an engagement announcement looks imminent
MailOnline has set out the 11 main reasons why their engagement is believed to be imminent.
Speculation has been ramped up in recent weeks that Harry could have proposed to the 36-year-old US actress, with the couple said to be 'head over heels' in love.
Today there were also unconfirmed claims online that Buckingham Palace had called in the majority of staff for an emergency meeting related to the prince.
Google even jumped the gun by referring to the Duchess of Cambridge as Meghan's sister in law when search using the Suits star's name.
Meghan Markle is moving her dogs to the UK in the clearest sign yet that she is planning to live in London with Prince Harry.
The 36-year-old US actress, who has been dating the prince since last summer, is known to be extremely fond of her labrador-shepherd Bogart and beagle Guy.
Prince Harry, 33, is also said to have become very attached to the dogs while visiting Miss Markle, who lets them sleep on her bed and feeds them on an organic diet.
"The fact she's started the process of moving them to England is the clearest hint yet that she sees her future living in London with Harry," a source said.
3. Bookies stop taking bets
Bookmakers have now decided to pull all bets on if and when the engagement will take place.
Last night Jessica Bridge of Ladbrokes said: "We have closed all betting on Harry and Meghan following rumours an announcement is imminent.
"With Meghan residing in London now it looks like their engagement announcement is coming sooner rather than later."
Paddy Power was still offering odds of 2-1 on a 2018 wedding, and a spokesman said: "It looks like the Prince is in a hurry to marry, the way he and Meghan Markle are ramping things up."
4. Removal vans spotted outside her Toronto home
Meghan Markle's plans to relocate to the British capital emerged when she moved out of her apartment in Toronto, with removal vans reportedly seen outside.
According to the reports, Meghan will be moving into Harry's cottage in the grounds of Kensington Palace.
Meghan and Harry were swept into Buckingham Palace in a Ford Galaxy with blacked out windows last month for tea with the Queen.
The actress was meeting Her Majesty for the first time and it is the Queen who must give Harry permission to marry because he is fifth in line to the throne.
The prince had desperately wanted his grandmother to meet divorcee Meghan and it would suggest that the couple are making plans for a future together.
Everything about the teatime meeting was deliberately informal, the Mail learned, in part it was to settle any nerves Meghan might have felt but also to ensure it was not widely publicised within the palace.
9. Meghan's car is in London and her possessions shipped
The ex-Suits star has bought herself a VW Golf to drive around London as she prepares for life in the UK.
She also brought clothes and important possessions but the remainder of her furniture and other belongings are being shipped over from Canada.
The last time an attractive young woman linked to a Prince was seen being driven through the streets in a flash car was when a certain Kate Middleton was pictured in an Audi A3 before her engagement to William in 2010.
10. Lands in London and goes straight for a facial
Following a seven-and-a-half hour flight from Toronto, Meghan Markle treated herself to a touch of retail therapy and facial treatments at a very exclusive spa.
On Tuesday Meghan, 36, was seen carrying a bag from the Sarah Chapman spa in Chelsea and was accompanied by the celebrity facialist herself as she left the beauticians.
It is no wonder that Chapman's Skinesis Clinic was top of Meghan's list when it came to skin treatments with the spa boasting an all-star clientele including Victoria Beckham and Gigi Hadid.
