Mr Tusk will head to London for a meeting with the Prime Minister on Tuesday after having a pre-briefing with the EU's chief Brexit negotiator Michel Barnier.
It comes further Brexit talks in Brussels saw little progress, with Mr Barnier saying the UK had to settle its obligations to the EU before talks of a transition of future relationship but Brexit Secretary David Davis insisting there are "no excuses" for moving forward.
The meeting with Mr Tusk will be seen as a key opportunity for Ms May to direct her message to member state leaders, whom she wants to push EU Commission negotiators to allow progress.
The Council will meet next month to decide whether "sufficient progress" is being made for talks to move on to discussion of a future trade deal.
In her speech in Florence on Friday the PM said she wanted a two year transition period in which Britain would stay in the single market, to provide "certainty" for business.
A positive initial response raised hopes the move would encourage the EU to begin talking about an essential EU trade deal, but on Monday Mr Barnier said talk of a transition could not precede talks on settling the divorce bill, and issues around EU citizens' rights and Ireland.
He said he was "keen and eager" to understand how the Prime Minister's speech would be turned into a negotiating strategy.
"We do not need to remind ourselves that we are six months into the process. We are getting closer to the UK's withdrawal and I think that this moment should be a moment of clarity," he said.
Mr Davis said the latest citizens' rights would be incorporated fully into UK law, progress had been made on resolving the Irish border and insisted the UK would "honour commitments" made during its EU membership.
"But it's obvious that reaching a conclusion on this issue can only be done in the context of and in accordance with our new deep and special partnership with the EU," he added.
"The UK is absolutely committed to work through the detail. We are laying out concrete proposals and there are no excuses for standing in the way of progress.
"It will take pragmatism on both sides to make headway and I hope we can achieve that this week."