The Prime Minister refused to rule out proposals the so-called transition period could be extended beyond 21 months during a number of crunch Brexit meetings in Brussels.
The plan would see another Britain’s attachement to the EU not end until December 2021, despite voting to leave almost five years previously.
A senior EU official confirmed Mrs May told counterparts at the European Council summit she is ready to consider extending the transition period as a possible solution to the Irish border impasse.
They added the Prime Minister hadn’t brought any new proposals to the table with her.
“There was no new proposals,” the source said.
“She also mentioned the transition period.
“She said the UK would be ready consider the extension of the transition period.”
European Parliament President Antonio Tajani, who also gave a speech to EU leaders, said the proposal was raised by both sides but the Prime Minister remained “neutral” about the option.
He said: “Both sides mentioned the idea of an extension of the transition period as one possibility which is on the table and would have to be looked into.
“Mrs May recalled the importance of a UK-wide customs territory. But we are defending the single market.”
The proposed extension emerged out of high-level meetings between European Commission and UK officials as a possible solution to the Irish border, which continues to plague negotiations and leave them at a standstill.
The deeply-controversial plans would see the so-called transition period extended by more than 20 months, meaning Britain would be forced to accept the bloc’s rules while remaining a member of its single market and customs union.
This would include the continuation of free movement, which risks infuriating Brexiteers who have called for its immediate end in March 2019.
While the proposal is yet to be put in writing by either side, the clause would also mean Britain would have to fork up more money to the so-called Brexit divorce bill, which currently stands at £39bn.
The Prime Minister told her EU counterparts “now is the time” to secure a deal ahead of her meetings.
“We’ve solved most issues in the withdrawal agreement,” she said.
“There’s still the question of the Northern Irish backstop but we can achieve a deal.
“A deal is in the interests not just of the UK but also of the EU.”