The UK has until March to secure a deal on the terms of its exit from the EU.
Mrs May was left livid last week after European Union president Donald Tusk used a meeting of leaders in Salzburg to rule that the Chequers plan "will not work".
Speaking to reporters on her way to NY to attend the United Nations General Assembly, May said she welcomed comments from European Council President Donald Tusk that the bloc still wanted to strike a deal, but added that the onus was still on the EU to break the deadlock on Chequers.
"We assume that a compromise will be reached (even though we may have to wait for that until five minutes to midnight) and a hard Brexit will be avoided".
More than half the Cabinet are reportedly in favor of a similar deal that would be modeled closely on the free trade agreement Canada operates with the EU.
The newspaper said that two senior members of May's Downing Street political team began "war-gaming" an autumn vote to win public backing for a new plan, after her Brexit proposals were criticized at a summit in Salzburg last week. He added that the Prime Minister should call another general election following her break-down in talks with Brussels.
She told journalists: I've always said no deal is better than a bad deal, and I think a bad deal, for example, would be something that broke up the United Kingdom.
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"We would like the Prime Minister to change tactic and to move towards a more Canada-style free trade agreement".
But speaking to BBC World at One, Mr Francois said: "We've yet to know what the final deal looks like but if it is based on Chequers then myself and my colleagues in the ERG could not vote for Chequers because we believe it doesn't represent Brexit".
'It would be the first free trade deal in history that increased barriers to trade and did not reduce them, ' she said.
"Failing that, all options are on the table".
The veteran leftist is expected to dodge direct commitments on the toxic issue, and instead advance a radical domestic agenda built around themes of social justice.He hopes it will appeal to voters who could be heading to the polls if Prime Minister Theresa May's government collapses under the pressure of Brexit before Britain is set to leave the European Union in March.