The Prime Minister’s meeting was confirmed by Downing Street on Monday evening.
It will be Mrs May’s final throw of the dice ahead of Tuesday’s Commons vote on her Withdrawal Agreement.
One of those Tory Brexiteers, Iain Duncan Smith, responded to the news by telling the BBC “I think they are reaching the point where they are about to have some kind of agreement”.
However, he added his support – and that of the influential European Research Group – would be dependent on the verdict of its “group of legal people” which will pore over any proposal coming out of Strasbourg.
A statement to the Commons by Brexit secretary Stephen Barclay has been put back to about 10pm as a result of Mrs May’s talks.
The negotiations are a boost for Number 10 after Michel Barnier, the EU’s chief negotiator, said earlier on Monday there would be no more high-level backstop talks.
Mr Barnier had claimed the only talks that mattered were “between the Government in London and the Parliament in London”.
Mrs May had earlier ducked a demand from Labour leader Jeremy Corbyn to update the House of Commons on the progress of negotiations, sending Brexit minister Robin Walker to respond to his urgent question in her place.
If her deal is defeated on Tuesday, MPs will then vote on Wednesday whether to support a no-deal Brexit.
If a no-deal Brexit is rejected, members will get a vote on Thursday on requesting an extension to Article 50 and delaying EU withdrawal.