"We are working to ensure that we have that future relationship in place by the end of December 2020", May said as she arrived at European Union headquarters in Brussels on Thursday for meetings on migration, security and other issues.
He said the sticking point in the talks was the issue of how to sort out the Irish question.
The EU says the solution is to keep Northern Ireland inside a customs union with the bloc, but Britain rejects that because it would mean customs checks between Northern Ireland and the rest of the UK.
The Prime Minister was due to address leaders of the 27 remaining EU states before they discuss Brexit in her absence at the European Council on Wednesday evening.
Ms May had also signalled she would consider extending the transition period "for a matter of months" after Britain leaves the European Union in March.
An extended transition period would not solve a fundamental problem with the EU's backstop proposals, the DUP said.
At present the two sides are proposing that Britain remains inside the European Union single market and is still bound by its rules from the time it leaves the bloc in March until December 2020, to give time for new trade relations to be set up.
"Imagine a situation whereby those opposing a deal would be able to say, as a result of a vote in the House of Commons, not only would that deal be defeated, it would also bring down the Irish Government, so I'm not sure if Deputy Martin really thought that through".
"But I am still optimistic that we can find a solution for the Brexit issue in the coming weeks or months".
Failure to meet in November could see a draft Brexit deal pushed back to a December summit, leaving little time for its ratification by the British and European parliaments.
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The leaders were very clear [at the summit in] Salzburg that they had hoped for virtually an agreement on the withdrawal agreement having been reached by now and that could have been formalised and finalised in this November summit.
"It would be very hard to tell the British people that we are extending another year or more into the implementation phase, and we're then going to pay tens of billions of pounds over when we actually say we need it for other domestic programmes", he told the BBC. Under the current proposal, the United Kingdom would effectively be a non-member: it would remain part of the single market and customs union, but would no longer be represented in EU institutions.
"And now the issue of Ireland remains open", Barnier added.
If May loses, there would be a leadership contest with the victor becoming prime minister, without the need for new elections.
The French Government yesterday published draft no-deal legislation that could require British citizens to obtain a visa before travelling to France following the UK's withdrawal from the EU. May says this new would destroy the constitutional integrity of the United Kingdom, by putting a customs border between Northern Ireland and the British mainland.
She also faces a rebellion from her parliamentary partners, Northern Ireland's Democratic Unionist Party, which has threatened to vote against her government's budget if she concedes to the EU's demands over the backstop.
Britain needed "to decide finally what they want and to rally behind the Prime Minister all together, not split", she said, adding: "Today we do not know what they want".
"I am open to the idea of an extension or a longer transition period, but that's not an alternative to a legally binding Irish backstop, so it's certainly not an alternative; it's something that might be part of the mix", he said.
But any extension will need to take into account concerns on both sides to avoid the transition ending with no deal.
"We are in a negotiation but at the moment it begins to look more like a capitulation than a negotiation".