Tackling Ms May at the weekly session of prime minister's questions, Jeremy Corbyn noted she had not mentioned "Chequers" in either her conference speech or in a recent update to the Commons on the state of the negotiations.
But, in her reply, Ms May said: "He asked me if the Chequers plan was dead, the answer is no."
Arriving at the EU summit, the prime minister said she believes a deal on the UK's orderly withdrawal from the EU remains "achievable", despite the deadlock in negotiations.
Ms May 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.
But leaders were openly saying that there would be "no breakthrough" at the summit, which was long billed as the "moment of truth" when a deal must be done to give time for ratification by the date of Brexit on March 29.
To follow the events as they unfolded, see our liveblog below
Welcome to The Independent's politics liveblog, where we will be bringing you the latest updates throughout the day.
Significant issues need to be resolved before a Brexit deal can be agreed, Irish deputy prime minister Simon Coveney has said.
He told the Today programme: "A lot of work has happened over the last two weeks that have actually found ways of closing gaps and getting agreement.
"But there are a small number of remaining issues. They are significant issues, so we shouldn't downplay them, that need to be resolved."
Regarding setting a date for a crunch EU Brexit summit next month, Mr Coveney said: "I think what's more likely is that dates will be suggested, but that there won't be a commitment to a new summit unless there is a signal from the negotiating teams that there is something to sign off on.
"And I think that's sensible. What we don't want to do is create drama around the build-up to a new summit date and not actually have something to sign off on.
"Both sides want to get a deal done here, and I think we need... to allow the negotiating teams to set the pace with a view to making recommendations, hopefully by mid-November, that a new summit is necessary to sign off on a final deal."
Referring to reports that EU chief negotiator Michel Barnier is open to extending the UK's transition period by a year, Mr Coveney said: "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.
"Everybody is agreed that that's where we need to get to. And, I think, Michel Barnier has shown a willingness to think imaginatively, and to show flexibility to get there.
"There needs to be a backstop that's there unless or until something better can be negotiated or agreed.
"And what Michel Barnier has indicated very clearly is that the EU side, certainly, is willing to allow more time in the transition period to agree an alternative solution to a backstop."
EU's chief Brexit negotiator, Michel Barnier, has reportedly said he is open to extending the transition period by a year in exchange for a compromise around the Irish backstop issue.
The president of the European Council has warned that there are “no grounds for optimism” ahead of a moment-of-truth Brexit summit in Brussels on Wednesday.
Donald Tusk said Theresa May needed to put forward “concrete proposals” if she wanted to avoid a no deal, after it emerged that leaders will not even consider plans for a trade deal with the UK because of the impasse.
More here from our Europe correspondent Jon Stone:
My colleague Rob Merrick is watching the Brexit committee this morning, where a number of senior civil service figures are being grilled by MPs.
Jeremy Corbyn is facing an explosive claim that he congratulated the Leave campaign on its “good work” during the referendum, while publicly opposing Brexit.
See our story here:
My colleague Ashley Cowburn is watching the work and pensions committee, where the permanent secretary is describing the scale of the universal credit reforms.
The big story of the day is the European Council summit in Brussels, where Theresa May is due to address other European leaders.
The PM will have separate meetings with European Commission President Jean-Claude Juncker, European Council President Donald Tusk and Irish Taoiseach Leo Varadkar before addressing the EU leaders in Brussels on Wednesday evening, Downing Street said.
The summit was seen as a "moment of truth" gathering for the Brexit deal, but the talks are deadlocked over the future of the Irish border.
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