However, the plan faced criticism from within her own party, and triggered the resignation of Foreign Secretary Boris Johnson, who recently referred to her plans as a "suicide vest".
But Gove himself offered a strong hint that he wants May's Chequers Brexit proposal - which has been criticised by hardline Brexiteers for being too soft - to be revisited and made tougher after Britain leaves the EU.
European Union negotiators are rewriting a key part of the divorce agreement, looking for a solution to avoid a sea border between Northern Ireland (which is part of the UK) and mainland Britain.
The fate of May's government and her Brexit plan is in doubt because it is unclear whether she could command the 320 votes she needs in the House of Commons, the lower house of the British parliament, to approve a deal. "The ancestors of many people we represent fought alongside the British in two world wars, but are now forced to stand aside in favour of people with no connection to the United Kingdom".
Mrs May has repeatedly said that the only alternative to her Chequers plan is a no deal scenario, an outcome with International Monetary Fund said could be disastrous for the UK's economy.
But the European Union, in a note before Barnier briefs ministers from member states on Tuesday, said both sides still have work to do to settle a range of issues, including the Irish border.
The International Monetary Fund has warned that a "no-deal" Brexit on World Trade Organization terms would entail substantial costs for the United Kingdom economy.
But with time running out for London and Brussels to thrash out a deal, Britain is preparing plans for a no-deal Brexit.
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That was the cue for Hazard to take charge, scoring on 37, 44 and 80 minutes, the last goal coming from the penalty spot. The scorer, predictably enough, was Wilfried Zaha, who marked his return from injury with a stunning solo effort.
But Mrs May said it was the government's job to "make sure we make a success of no-deal, just as we make a success of getting a good deal".
The report also said the Treasury and Bank of England should be prepared for the possibility of "sharp declines in sterling and other asset prices" and the Bank should be ready to act to ensure the financial system has adequate liquidity.
She agreed previous year for Northern Ireland to stay locked in the bloc's Single Market if the border can not be kept open. Signs are growing that the party has no intention of bailing the Prime Minister out.
With just over six months until Britain is due to leave the 28-nation European Union on March 29, the two sides still have big gaps to bridge in divorce negotiations, and May's Conservative government remains divided over how close an economic relationship to seek with the bloc after Brexit.
Requirements for a "backstop" arrangement at the Irish border, contained in December's agreement between Mrs May and European Commission president Jean-Claude Juncker, would leave the United Kingdom a "vassal state" of the EU, the former foreign secretary warned.
According to a Comres survey, 50% of British adults feel the overall impact will be negative, whereas 41% think it will be positive.
The People's Vote campaign, meanwhile, claimed a "fresh wave" of 18-year-olds becoming eligible to vote was "transforming the dynamics of the Brexit debate" because they mostly back staying in the EU.