Theresa May has said that the idea of extending the Brexit transition period "for a matter of months" has been considered.
But the Prime Minister said she did not expect the option to be used as the UK and EU are working to have their future relationship in place by the end of 2020.
"In those circumstances there would be no need for any proposal of this sort and I'm clear that I expect the implementation period to end at the end of December 2020," Mrs May told reporters in Brussels on Thursday.
The prime minister is facing a backlash from Brexiteers over extending the transition period, which it has been suggested could be be extended to the end of 2021.
The idea was floated by EU chief negotiator Michel Barnier to give time to resolve the intractable problem of the Irish border.
If agreed to the end of 2021, the change would mean the UK remaining within the single market and customs union and subject to EU rules and regulations for almost three years after the official date of Brexit in March 2019, and more than five years after the referendum vote to Leave.
Mrs May said that the UK had already put forward a proposal to avoid the need for either a hard border or a customs border down the Irish Sea.
And she added: "A further idea that has emerged - and it is an idea at this stage - is to create an option to extend the implementation period for a matter of months - and it would only be for a matter of months.
"But the point is that this is not expected to be used, because we are working to ensure that we have that future relationship in place by the end of December 2020."
She added: "We are working with the European Union to deal with this issue of ensuring that if there is a gap between the end of the implementation period and the point at which the future relationship comes in - we don't expect a gap to exist, but if there is we want to ensure there's no hard border between Northern Ireland and Ireland."
Furious Brexiteers said that the move would delay yet further the moment when the UK could sign new trade deals around the world, and would cost taxpayers billions of pounds in additional contributions to the EU.
Shadow Chancellor John McDonnell said he was against extending the transition period, saying it would cause economic uncertainty to "drag on".
The remaining EU 27 leaders said in a joint statement that that it was "not planning to organise an extraordinary summit on Brexit in November" as things stand due to a lack of progress in the negotiations.
As unrest within Tory ranks continued, MP Nadine Dorries repeated her call for former Brexit secretary David Davis to replace Mrs May as leader.
“We cannot find the money to fund our frontline police properly, we cannot find the £2 billion for the vulnerable on Universal Credit, but we can mysteriously find billions to bung to the EU for the unnecessary extra year Clegg and Blair asked Barnier for to waylay Brexit,” said Ms Dorries.
And Mr Davis’s former chief of staff Stewart Jackson asked: “If you can’t – or in the EU’s case won’t – resolve the backstop issue now because it’s an issue of principle than why will it take another three years to resolve it? Will it not be an issue of principle once we have coughed up billions more in UK taxpayers’ cash?”
Leaders of the 27 remaining EU leaders ditched proposals for a special Brexit summit in November, after chief negotiator Michel Barnier told them he needed “much more time” to find a way to avoid a hard border in Ireland.
With just 160 days to go to the official date of Brexit, Mrs May urged the EU27 to find a “creative” way out of the current dilemma.
“We have shown we can do difficult deals together constructively,” the PM said. “I remain confident of a good outcome.”
And she told them: “The last stage will need courage, trust and leadership on both sides.”
After her Chequers plan for Brexit was humiliatingly rejected in Salzburg last month and efforts to seal a last-minute deal foundered last weekend over the EU’s demand for a “backstop” arrangement for Ireland, Mrs May was fighting to keep the door open for an agreement to deliver an orderly withdrawal.
EU leaders gave her 20 minutes to make her pitch before discussing Brexit in her absence over a dinner of turbot cooked in wheat beer.
The president of the European Parliament, Antonio Tajani, 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 initially suggested an “implementation period” of around two years after Brexit, to give the UK’s authorities and companies time to prepare for the new arrangements.
But she later accepted a 21-month transition offered by the EU, ending on the last day of December 2020.
It emerged on Wednesday that Mr Barnier was ready to discuss a further year’s extension to allow time to find a solution to keep the Irish border open.
This week’s summit had been billed as “the moment of truth” when agreement was needed to allow time for ratification in the Westminster and European parliaments.
But Mrs May did not come forward with the new “concrete proposals” on the border issue which European Council president Donald Tusk said were needed to break the deadlock.
While expressing their willingness to work for an orderly UK withdrawal, a number of EU leaders said their countries were beginning preparations for a no-deal Brexit.
In a speech to the German parliament before travelling to Brussels, Chancellor Angela Merkel said that the possibility of a Brexit deal was “still there”, but added that Berlin was making plans for a no-deal withdrawal.
And in Paris, Emmanuel Macron’s government published details of legislation to authorise preparations for a no-deal Brexit, which could see the restoration of customs checks and health inspections for animals at French ports, and even a requirement for Britons to seek visas for stays of three months or more.
Mr Macron, who held separate talks with Mrs May ahead of the three-hour dinner, said it was time to “accelerate” talks.
But Lithuanian president Dalia Grybauskaite said there would be “no breakthrough” this week because Mrs May lacked a strong mandate from her party and parliament.
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. They do not know themselves what they want. It is a problem.”