The prime minister is understood to have confirmed an interview with Holly Willoughby and Philip Schofield on the ITV show before next week's general election, with discussions ongoing over the timing of his appearance.
But the move comes amid a row over Mr Johnson's continued failure to take part in a 30-minute one-on-one interview with Mr Neil, the fearsome BBC interrogator.
Labour claimed the prime minister had broken an explicit agreement made between all the political parties and the BBC for a series of leaders' interviews conducted by Mr Neil.
Jeremy Corbyn and the SNP's Nicola Sturgeon have both already faced Mr Neil, with Jo Swinson, the Liberal Democrat leader, and Nigel Farage, scheduled to take part in individual interviews later this week.
The Labour leader had a tough time against Mr Neil, who repeatedly demanded apologies for Labour's antisemitism crisis. Ms Sturgeon also endured a difficult grilling over her domestic record in Scotland.
The Conservatives insist discussions are ongoing with the BBC over the interview but with less than two weeks to go until the election, time is running out to reach an agreement.
Mr Johnson referred to the row when he appeared on the BBC's Andrew Marr Show, saying: “I am perfectly happy to be interviewed by any interviewer called Andrew from the BBC." However he stopped short of confirming it would take place.
His response has been disputed by Mr Neil, who tweeted: "There are not really any negotiations going on.
"We’re simply waiting on a date, time and venue. As we have for several weeks. So far — not a sausage."
Meanwhile, Channel 4 has been cleared by the regulator after it infuriated the Tories by using an ice sculpture to stand in for Mr Johnson during a debate on climate change.
Ofcom said the prop "was not a representation of the prime minister personally", and that "little editorial focus was given to it, either visually or in references made by the presenter or debate participants".
The Conservatives complained that the broadcaster failed to allow the former environment secretary Michael Gove to be its representative for the debate.
A source at ITV said they were hoping to get all the main party leaders to appear on This Morning before the election next week.
Mr Corbyn appeared on the This Morning sofa on Tuesday, where he apologised for the handling of antisemitism in the Labour party, saying he is "very sorry for everything that has happened".
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