The announcement will be formally made by May on Friday, during her highly-anticipated Brexit speech in the Italian city of Florence, the FT said.
But it is understood that Johnson considers it could be a resigning matter if May veers towards the kind of "soft Brexit" advocated by Philip Hammond, the chancellor, when she makes a key speech in Florence on Friday.
Friends of Johnson told a newspaper yesterday he "could not live with" the version of Brexit under consideration, which prompted the publication of his personal vision for Brexit on Saturday.
The Foreign Secretary told reporters in NY he would not resign and denied that ministers were split over Brexit policy, insisting: "We are a nest of singing birds".
Ms Patel told Sky News: "I'm for Brexit and that's what the PM is trying to achieve - she's been clear, the Cabinet is clear that we want best deal for Britain". "And he knows perfectly well that, normally, a foreign secretary would be sacked instantly for doing that".More news: Man U join City at top of the EPL
In a sign of the growing frenzy around his intentions, the Foreign Secretary was cornered by TV cameras as he entered a lift in his NY hotel on returning from a jog, and forced to deny he was planning to resign.
But Mr Johnson has attempted to play down such claims, as he denied that his decision to publish the piece was a challenge to the Prime Minister.
The foreign secretary did not name fellow Telegraph scribe Nelson as the man who grabbed his attention with a piece titled: "There are three theories why Boris Johnson is lying low, and none is flattering".
And asked directly if he would resign, he replied: "No".
She also confirmed that Downing Street had not given Mr Johnson's magnum-opus the go-ahead.
If Britain remains in the single market, it would continue to pay for access and would need to abide by European Union rules and regulations, including freedom of movement.
Mr Hogan, an Irish politician who is the EU's agriculture commissioner, said in an interview with the Evening Standard, "clearly, he [Mr Johnson] is not directly involved in the negotiations on behalf of the British Government with the European Union".