Britain has proposed staying temporarily aligned to the EU's customs rules, but the bloc wants this to have no end date - something her eurosceptic MPs will not accept.
The PM said: "We have shown we can do hard deals together constructively".
But, more importantly for Mrs May, he also offered her some political top cover against the cries of betrayal coming from some Brexiteers, pointing out that in September last year during her Florence speech the prime minister talked about a transition period of "around two years" - the current transition proposal is 21 months, leaving Mrs May some space to move.
The "backstop" refers to a commitment from both sides that even if Britain exits without a comprehensive deal, there will never be a hard border between Northern Ireland, which would leave as part of the United Kingdom, and the Republic of Ireland, which will remain part of the European Union.
After Brexit talks broke down last weekend, French President Emmanuel Macron said on Monday, "I believe in our collective intelligence, so I think we can make progress".
"We have always said that we are happy to show flexibility in terms of how we get to a destination where-by there is a backstop, or an insurance mechanism, in place to reassure people on the island of Ireland that they are not going to see the re-emergence of physical border infrastructure".
"We hope extended transition will not be needed", May added.
May emphasised she did not expect the extension to be needed beyond the current date of December 2020, amid anger among eurosceptic members of her Conservative party that Britain could be tied to the European Union indefinitely.
All of those mileposts are on the drive toward March 29, when Britain will officially exit the European Union, triggering a transition period that will last through 2020.
But a longer transition would not necessarily resolve the backstop issue, which must be included in the withdrawal treaty and ratified before the end of March to avoid the damaging "no deal" scenario. Officials have said a deal could be struck as late as the European Council's December summit, with both sides determined to avoid no deal.
But later on Thursday, she attempted to play down the comments and said Britain will not be pushing for an extension to the Brexit transition period. Others at the bar managed to capture videos of the four leaders enjoying themselves and, naturally, posted them online. "I remain confident of a good outcome".
Talks on finalising the UK's withdrawal agreement and a political declaration on future trade relations with the EU have been blocked by failure to agree on a backstop to avoid a hard border between Northern Ireland and the Republic in the event that an agreement on future EU-UK relations can not be struck.
The proposed 12-month extension would cost billions of pounds in EU fees and leave Britain under European rules for nearly six years after the referendum result.
However, an extension does not in and of itself solve May's problem, which is that she has yet to fully decide, let alone agree, what sort of relationship she wants to secure during that additional transition period.
The move, which would effectively prolong the terms of Britain's European Union membership, could potentially break the impasse.
However, the lack of progress on the backstop for Northern Ireland has put those processes on hold. Neither would be supported by the House of Commons.
Bertie Armstrong of the Scottish Fishermen's Federation said: "The EU must not be permitted to misuse the time when the United Kingdom is in the Brexit waiting room to try to place conditions on the return of fish stocks that are rightfully ours".