However DUP leader Arlene Foster refused to accept any terms which would see Northern Ireland leave the EU on different terms to the rest of the UK after Mrs May proposed aligning the state with the Republic.
The PM has now cleared her schedule for crunch talks in Westminster, as well as with leaders in Brussels and on both sides of the Irish border.
Next week Mrs May will put forward her final offer to the EU before the December summit on Thursday and Friday.
A deal will need to be in place with Dublin and Stormont by the end of this week, however, with Mrs May expected to return to Brussels on Friday.
With little work expected over the weekend – especially given the DUP’s refusal to carry out talks on Sundays due to their religious reliefs – the next four days will be crucial.
Mrs May could return to Brussels as soon as tomorrow as the clock keeps ticking on Britain’s Brexit countdown.
Check back throughout the day for live updates below as Mrs May fights to save Brexit.
Theresa May has four days to come to a Brexit agreement
5.30pm – Juncker’s diary could cause problems…
European Commission chief Jean-Claude Juncker has confirmed he is “very confident” of securing a deal – but could his absence at the end of the week upset the progress of Brexit talks?
He said: “I will have a meeting with the PM in the course of this week. Maybe tomorrow, maybe the day after tomorrow – not on Friday and Saturday because I’m out of town – maybe on Sunday.
“We’ll have a meeting and we had a good constructive meeting yesterday. I’m very confident that we’ll do it.”
5.20pm – Foster blames Irish Government for Brexit text delay
Mrs Foster has accused the Irish Government of blocking Theresa May from sharing information about plans for the Irish border with the DUP.
She told Sky News: “There have been reasons given to us as to why we didn’t receive the text until later on.
“One of those reasons apparently is because the Irish Government wouldn’t allow them to share that text and in many ways I can understand that.
“But the important thing is once we had seen the text we knew that it would not fly for Northern Ireland, for Scotland, because once you start separating parts of the UK out then it has ramifications in other places as well.”
She added: “The Irish Prime Minister…