According to the newspaper, Merkel and President Macron have urged the EU's chief negotiator Michel Barnier to guarantee that Europe will not impose a customs border in the Irish sea in order to give May room to sell the deal back home.
But with Brexit talks at an impasse, the bloc has suggested extending that period, to give more time to strike a trade deal that ensures the border between Northern Ireland and the Republic of Ireland remains friction-free - the main sticking point to a Brexit deal.
The Prime Minister then said an extension could resolve the Irish border issue and help the nation get a deal with the EU.
TRANSITION Such an extension would be hard for May to sell at home, where her overall strategy has been criticised by all sides - Brexit campaigners accuse her of making Britain a vassal state, European Union supporters say the offer is the worst of all worlds and others are increasingly frustrated over the talks.
He also told reporters on the third day of European Union summit meetings in Brussels that it would be up to British Prime Minister Theresa May to decide whether she had to defy opposition from her unionist Northern Irish allies and agree to the EU's proposed backstop, which would potentially create trade barriers between Northern Ireland and the British mainland.
Mr Barnier said there was absolutely no intention by European leaders to punish Britain.
British Prime Minister Theresa May and her closest advisers were on Thursday contemplating how to scale the "brick wall" that is preventing a Brexit deal being agreed with Brussels.
If progress had been made at the European Council meeting of leaders, an extra summit was expected to be held in November to sign off the deal.
"I want to be optimistic because the political message of Mrs".
Juri Ratas, the Estonian Prime Minister, struck a more sympathetic tone.
"I'm open to the idea of an extension or a longer transition period, but that's not an alternative to a legally binding Irish backstop".
But she said she had found "a very real sense that people want that deal done" among her fellow leaders.
So if an agreement is reached - which suddenly sounds much more likely - the debate will shift to whether it can get through parliament or whether May can survive.
May 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.
Tory MP Nadine Dorries repeated her call for former Brexit secretary David Davis to replace Mrs May as leader. In a recent speech, the newspaper reports that Scotland's first minister Nicola Sturgeon called for Scotland to be allowed to stay a member of the EU's single market, should Northern Ireland obtain a special deal.
At the start of a summit that had previously been earmarked as the deadline for a breakthrough, both sides admitted the deadlock would take more time to untangle and said they were willing to extend the post-Brexit transition until the end of 2021.
Varadkar also warned that a return of customs posts on Ireland's border with Northern Ireland could lead to violence returning to the British province.
"She accepted the dictates as to how the negotiations would take place and the sequencing of them by the European Union".
Before travelling to Brussels, Mrs May vowed to protect the "precious Union of the United Kingdom" as she answered questions in the House of Commons.
This week's Brussels summit had been set as the deadline for a draft deal, but European Union leaders have instead been left to contemplate the potentially catastrophic scenario of Britain crashing out in March without any agreement.
He added: "Leo Varadkar has taken a sledgehammer to the work which was done but even more worrying is his total disregard to the impact of his irresponsible and reckless rhetoric on the peace of Northern Ireland".