European Commission President Jean-Claude Juncker said he was more confident than before about a deal but added nothing would be decided before he had dinner with May on December 4.
The tweet follows Tusks meeting with Theresa May at the EU's Eastern Partnership Summit, where May was given a deadline of 4 December to make finalize the Brexit Bill in order to move forward with the next phase of negotiations. "May agreed to this time frame".
Tusk said it was still possible the other 27 European Union leaders would conclude at a summit on December 14-15 that Britain had made "sufficient progress" toward meeting three key conditions for them to approve the opening of trade talks in the new year.
"The UK will need to give credible assurances as to how to avoid a hard border before December 4, as it is still unclear how this can be done", the official added.
"This is. unsafe politically at a time when the country does not need an election", he said, in an apparent reference to the December EU summit. Any hurdles to the movement of people or goods could have serious implications for the economies on both sides, and for Northern Ireland's peace process.
"There are still issues across the various matters that we are negotiating to be resolved", May told reporters when leaving Brussels. "We have move to phase two on the basis of a credible road map or the parameters around which we can design a credible road map to ensure that it doesn't happen", he said.
"We are not going to allow a border to re-emerge on the island of Ireland, and we have a shared responsibility with the United Kingdom on that", Coveney added, saying a hard border would undermine the Northern Ireland peace process. We have the same desire.
For months, the EU's demand for Britain to pay something like 60 billion euros ($72 billion) has seemed the toughest nut to crack.
She said: That's not true.
Now, Ireland could be a sticking point.
"Without sufficient progress on the Irish issues that can't happen".
The EU-26 meanwhile threw its weight behind Ireland, as talks enter into a crucial phase before the EU summit in mid-December.
Speaking on arrival at an European Union summit in Brussels on Friday morning, the Irish Foreign Minister Simon Coveney said that leak was "unfortunate" and "not helpful".
Ireland wants guarantees from the United Kingdom that a hard border between Northern Ireland and the Republic of Ireland will be avoided.
Speaking in her rural Fermanagh and South Tyrone constituency, which overlooks part of the Irish border, Mrs Foster criticised the Irish government for demanding commitments from the United Kingdom before consenting to the next phase of Brexit negotiations.
Britain has rejected the former because it would divide Northern Ireland from the British mainland.