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.
Tusk says "what I feel today is that we are closer to the final solutions and the deal".
A United Kingdom source said the Prime Minister issued an appeal "to find a creative way out of this dilemma" on the Irish border and reiterated she was "fully committed to finding a legally operative backstop" that guarantees no hard border in Ireland.
An accord sketched by officials from both sides last weekend stalled because May's fractious government rejected a "backstop" insurance clause the European Union wants in case future talks fail to forge a trade pact that avoids customs posts on the Irish border.
The EU says the solution is to keep Northern Ireland inside a customs union with the bloc, but Britain rejects that because it would mean customs checks between Northern Ireland and the rest of the UK.
British Prime Minister Theresa May says the remaining differences on Brexit terms between the United Kingdom and the European Union are "few but considerable" - but she says she is confident the two sides will reach an agreement.
Britain has secured a 21-month transition period following the formal date of Brexit in March 2019, to give authorities and companies time to prepare for new arrangements.
She said 2 1/2 years after Britain's Brexit referendum, the country had still not explained clearly how it wants to leave the EU.
"And the European Parliament would not or should not approve a deal that undermines the single market and doesn't give Ireland what we need in relation to the backstop".
Sammy Wilson declared himself "appalled" with the Mrs May's handling of the negotiations, saying "she only has herself to blame" for the EU's "intransigent" stance.
That was a notably less optimistic assessment than the one given by European Commission president Jean-Claude Juncker, who on Thursday confidently predicted a deal "will be done".
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Mrs May, who had been called upon to table new proposals on the Irish Border backstop, was thought to have been "developing her thinking".
At the meeting in Brussels, EU leaders decided that not enough progress has been made in negotiations to warrant calling a one-off summit in November for a divorce deal to be signed.
"We need time to get ready for that".
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".
London is set to leave the European Union on March 29, 2019, although the bloc's leaders could agree to delay this.
"Nothing new tonight", Dutch Prime Minister Mark Rutte said after an evening when not exacerbating divisions with Britain was seen as a victory in itself.
Addressing reporters in Brussels, Mrs May said: "What has now emerged is the idea that an option to extend the implementation period could be a further solution to this issue of the backstop in Northern Ireland". But the problem is we can not have a border in Ireland between the Republic and the province [of Northern Ireland].
"We know how divided British politics is at the moment, not just the Government, and the Government party but also Parliament itself". They see little scope now for the European Union to move.
Tory MP Nadine Dorries repeated her call for former Brexit secretary David Davis to replace Mrs May as leader.
At a three-hour cabinet meeting on Tuesday morning, which included ministers with reservations about her strategy, May said a deal was possible if they all stood together.
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.