No 10 said Friday’s Florence speech was a “significant moment” and that the Prime Minister would welcome input from her most senior ministers before it is delivered.
That will come at a one-off cabinet meeting 24 hours earlier, giving Mr Johnson – and other Brexit rebels – a platform to try to water down concessions to Brussels.
The announcement of the meeting comes as the Foreign Secretary denied reports that he about to resign, telling reporters in New York: “Of course not.”
Meanwhile, Ms May said she was confident of achieving a consensus, saying: “Yes, the Cabinet is absolutely clear about the destination we are aiming for in relation to our European negotiations.”
Asked whether Mr Johnson should be sacked, the Prime Minister replied: “Boris is doing good work as Foreign Secretary. He has been doing that here at the United Nations.”
Her spokesman, asked if she believed Mr Johnson would remain in the Cabinet beyond the weekend, told reporters in New York: “Yes. Boris Johnson is the Foreign Secretary and, as the Prime Minister has said, he is doing a good job.”
The pair are both at the United Nations General Assembly, but are not – contrary to earlier reports – expected to meet today, the spokesman said.
It has been reported that Mr Johnson will not accept the UK making payments to the EU permanently in return for access to the single market.
He is also believed to be insisting that any transition period must end by December 2020 – and that money must only be paid during it in return for an assurance of a free trade agreement.
The Prime Minister has acknowledged that ongoing payments after departure in 2019 are “part of the negotiations” – and did not deny rumours of £10bn a year for three years.
However, there are suggestions that she will back off using her Florence speech to make a fresh offer to Brussels on the Brexit divorce bill, following Mr Johnson’s open challenge.
It is not clear whether cabinet members will be shown a full text of the Prime Minister’s speech when they meet at 10am on Thursday, in Downing Street.
But, asked to explain its purpose, a No 10 source said: “The Prime Minister has said consistently that she values the contribution of people from across the Cabinet.
“Clearly this is a significant moment in terms of our progress and in terms of our relationship with Europe”
Mr Johnson will be in the audience for Ms May’s formal address to the UN on Wednesday, but the two have not spoken since his explosive weekend article, setting out his different Brexit vision.
Caught on the way back from a run in New York, the Foreign Secretary dismissed claims that the cabinet is fatally split on Brexit, saying: “We are a nest of singing birds.”