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.
Speaking to France-Inter radio, Mr Barnier said the deal was "90%" done and he was hoping to complete it "in a few weeks or a few months, as soon as possible". "What I feel today is that we are closer to the final solutions and the deal", he told a news conference.
British Prime Minister Theresa May had earlier addressed her fellow leaders, indicating that she could accept extending the post-Brexit transition phase to take the heat out the deadlocked issue of the Irish border.
A Downing Street spokesperson said: "The UK Government regularly engages with the Northern Ireland parties on a range of issues, including on EU Exit, and will continue to offer these engagements".
May's plans have been criticized by all sides at home - Brexit campaigners accuse her of making Britain a vassal state, European Union supporters say they offer the worst of all worlds and others have expressed frustration over the lengthy talks.
If agreed, the change would mean the United Kingdom remaining within the single market and customs union and subject to EU rules and regulations for nearly three years after the official date of Brexit in March 2019 and more than five years after the referendum vote to Leave.
Lidington rejected claims that an extension would cost Britain more than $13.1 billion USA in payments to the European Union in order to stay in the bloc's single market and customs union for another year.
The transition period, which would come into force when Britain officially leaves the EU in March 2019, is meant to be a temporary arrangement to continue the current UK-EU relationship while a future trade deal is negotiated. 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.
"She said that her aim was to wrap this up in November", one of the business people listening to the call said.
"But I believe everybody around the table wants to get a deal".
"I am going to ask Prime Minister May whether she has concrete proposals on how to break the impasse", EU President Donald Tusk declared.
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"I am still cautiously optimistic [about the deal]". But May's team is "considering the move", because it would be a "simple way to buy more time to agree a UK/EU trade deal, which is meant to remove the need for the Irish border backstop guarantee".
"Northern Ireland voted Remain and there is also a majority support for the backstop".
Now this agreement, during which non-member Britain would continue to follow all European Union rules, would run until December 2020.
Stephen Martin, IoD director general, said the PM did not say if the possibility of extending the transition period was being seriously considered.
"As long as we don't have a solution we won't be able to explain exactly how it can succeed", she said Thursday. 'But only so many - and we have looked at all of them.
"We noted in particular the need to closely watch the situation in the Western Mediterranean, and in this context, to strengthen our cooperation with Morocco, as recommended by [Spanish] Prime Minister [Pedro] Sanchez", Tusk added.
The proposed extension was also criticised by Tory MPs, including arch-Brexiteer Jacob Rees-Mogg who branded the idea "a rather poor attempt at kicking the can down the road".
May addressed other European Union leaders before they gathered for a dinner of pan-fried mushrooms and turbot in wheat beer - without her - to assess the state of Brexit talks. Barnier emphasised the "unanimity on the part of the EU" that there should be no closed border between Northern Ireland and the Republic of Ireland.
May said the United Kingdom was considering an extension of several months.
The chaos promised by "no deal" is very much in the minds of officials on both sides of the Channel.