The Prime Minister has insisted an exit agreement is still "achievable" despite negotiations stalling just days ahead of a crunch summit.
But Mr Tusk said they would need to believe that a deal was almost done - and without some new move from Mrs May today, that belief seems unlikely to come this week.
"Not just the speech but also the answers that were given to a number of questions in the Commons, they indeed, for our chief negotiator, demonstrate that finding an agreement will be even more hard than one could expect", the official said.
On Tuesday, European Council president Donald Tusk called the border "a new version of the Gordian Knot"-the Ancient Greek metaphor for a problem that seems utterly intractable".
Officials said they expected the European Union leaders to tell her they have little more to offer since talks stalled on Sunday and they will step up preparations for Britain to drop out of the bloc with no deal.
Raab, who replaced David Davis after he resigned from his post saying Theresa May's proposals for a deal with the European Union would not really deliver Brexit, flew out to Brussels on Sunday for surprise talks amid speculation that an agreement was imminent - but they broke down after little more than an hour, according to The Times.
Some EU diplomats speculate that she needs to have a fight in order to get the deal she does eventually deliver through a divided British Parliament.
Yesterday Theresa May came under fire from Leavers and Remainers as in Parliament she refused several times to say when a so-called Irish backstop arrangement would end in the event of no formal Brexit trade deal being reached. "We need more time, but there isn't much time left", one British official said.
Members of May's own party and the Conservatives' parliamentary allies oppose the prime minister's current proposals for the future EU-U.K. border in Ireland, putting her in a political straitjacket that restricts the "creative" ideas Tusk seeks.
Both sides say much of the withdrawal agreement, which sets the divorce terms for Britain's departure, has been agreed, but there are still outstanding issues, mostly on the backstop.
No new proposals are expected to be tabled or discussed this week and discussions are likely to continue at official level only.
Germany's Europe minister, Michael Roth, said Berlin's message to Mrs May was: "Take responsibility and be constructive".
Some signs of a looming agreement began to appear on Sunday mid-day after the publication of the statement by the UK's Department for Exiting the European Union stating that Brexit Secretary Dominic Raab is expected to visit Brussels as part of an unscheduled trip.
Nevertheless, the prime minister said on Monday that the two sides were not "far apart" and the border issue must not be allowed to derail the entire effort.
Barnier dropped a big hint the November meeting would not be approved when he told journalists: "More time is required to find this comprehensive deal and reach this decisive progress". We are all doing our jobs and we are trying to get the best deal for this country, and that's it.