Mr Tusk said that Theresa May declared "that it's almost impossible to trigger Article 50 this year"
Downing Street has insisted that the EU Council president's claim that Article 50 will be triggered early next year is only his "interpretation".
Donald Tusk let slip, at a summit in Bratislava, that Theresa May wants to begin the formal process to extract Britain from the EU by February 2017.
He said the British prime minister had told him during a meeting in Downing Street that she is likely to get the process of Brexit under way in around six months.
Speaking about his meeting with Mrs May, Mr Tusk told a summit news conference: "Prime Minister May was very open and honest with me.
"She declared that it's almost impossible to trigger Article 50 this year but it's quite likely that they will be ready maybe in January, maybe in February, next year."
But Downing Street has since down-played Mr Tusk's comments as nothing more than an "interpretation" of his meeting with Mrs May, who will not trigger Article 50 this year but "recognises the need to deliver on the public verdict without delay".
European leaders are keen for those negotiations to begin as soon as possible to end further uncertainty affecting the continent.
Theresa May has always insisted that Article 50 should not be triggered immediately as Britain needs to have the best negotiating team in place.
Formal negotiations between the UK and the EU cannot begin until she starts the two-year process, which Brexit Secretary David Davis has insisted will be triggered without a parliamentary vote.
Meanwhile, Defence Secretary Michael Fallon vowed to block any proposals for an EU army while Britain remains a member of the union, in a move likely to anger European leaders.
In his state-of-the-union address on Wednesday, European Commission president Jean-Claude Juncker called for EU countries "to pool their defence capabilities in the form of a permanent structured co-operation", and proposed a European Defence Fund by the end of the year.
But Mr Fallon said the UK would veto plans for any EU army that may rival NATO.