Mr Tusk will make the statement at 6.50am GMT on Friday but his office refused to release further details.
Earlier today the EU demanded a draft Brexit deal from Britain by Sunday if there is to be any hope of moving onto transition and trade talks at next week’s EU summit in Brussels.
The curious timing of tomorrow’s announcement suggests a deal could be on the table, and an early morning statement would give leaders across Europe an entire working day to come to terms with whatever Mr Tusk has to say.
And his statement, shortly before the markets open, suggests Mr Tusk’s speech could have financial ramifications.
BBC Political Editor Laura Kuenssberg said: “Tusk statement is just before the markets open tomorrow…. suggests it might have big financial implications, or maybe he is meeting someone for a big breakfast…who knows.”
Mr Tusk will leave for a visit to Hungary after delivering the statement on Friday but this still does not fully explain the reason for the early start tomorrow.
Meanwhile, an Irish official has told a British Irish Chamber of Commerce event in Brussels that negotiations are moving “very quickly” and a deal could be agreed within hours.
The official said: “It is moving quite quickly at the moment. Negotiations are continuing.
“I think we are going to work over the next couple of hours with the UK government to close this off. I say hours because I think we are very close.”
In Britain, Theresa May is still trying to negotiate the deadlock as is believed to be working through the night in order to have something prepared by the time Tusk makes his Brexit statement in the morning.
On Monday, the Democratic Unionist Party (DUP) scuppered Monday’s tabled deal over concerns about Northern Ireland’s post-Brexit status.
The party said the proposals, which aimed to avoid a “hard border” by aligning regulations on both sides of the border between Northern Ireland and the Republic of Ireland, were not acceptable.
Dublin insists it will not agree to any deal that includes a hard border, something Mrs May seems keen to ensure.
Yesterday the Prime Minister spoke to Irish Taoiseach Leo Varadkar and DUP leader Arlene Foster but does not appear to have made any concrete progress, with Westminster, Dublin and Stormont refusing to back down on their demands.
Diplomats from the EU27 are scheduled to meet on Friday in the hope an agreement will have been reached by then.
However, the progress of the Brexit agreement could still be interrupted by the calendar of European Commission President Jean-Claude Juncker, who is “out of town” on Friday and Saturday and therefore unavailable for talks.
Mrs May is also facing pressure from various groups in Westminster as the Brexit deadlock deepens divisions within the Government.
The Labour Party has this week branded the Government’s performance in Brussels an “embarrassment” and a “shambles”, while senior Brexit-backing Tories are unhappy about the idea of the whole of the UK signing up to any “regulatory alignment” with the rest of the EU, as they believe it would defeat the point of Brexit.
Brexiteers, including MP Bernard Jenkin, warned the House of Commons it would be impossible to strike trade deals with other nations if the UK “remains shackled to EU regulation after we’ve left the EU”.
And a group of 19 Remain-backing Tories, including three former cabinet ministers, have told the Prime Minister it is “highly irresponsible” for anyone to dictate terms which may scupper a deal.
In a letter to Downing Street, they accuse ardent Brexiteers of ignoring warnings about the uncertainty a no deal scenario would create.
The group, which includes Nicky Morgan, Stephen Crabb and Dominic Grieve, has urged the Mrs May not to rush into an agreement and concludes by telling her to “take whatever time is necessary to get the next stage of the UK’s relationship with the EU right”.