At a press conference in Brussels, Tusk said: "I hope we will be able to move to the second phase of our talks in December."
The UK government has been keen to progress to negotiations on the future trading relationship with the European Union, but talks have been hanging on the first phase, dealing with separation bills, including the much-discussed divorce bill.
But EU negotiators have previously bemoaned limited progress on the first round, and reiterated a commitment to maintaining the sequencing of negotiations.
May's new meeting with Tusk comes after it emerged there were indications that the EU's chief negotiator wants to know what offer will be on the table regarding the divorce bill, ahead of the European Council on 13 and 14 December, with Brussels no longer holding the UK to such a "strict ultimatum".
Earlier this week, the cabinet agreed the UK should offer to chip in more money to the EU, but not before the EU agrees to begin talking about a fresh trade deal.
The clock is ticking to progress with negotiations, after Britain served the EU with formal notice of Brexit in March kicking off a two-year countdown to the UK's departure in 2019.
And a new report from the Institute of Economic Affairs (IEA) recommends the UK make a partial offer on the Brexit divorce bill to take the next step, but withhold the final amount until a trade deal has been agreed.
Source : http://www.cityam.com/276389/theresa-may-gears-up-fresh-brexit-talks-donald-tusk-bid