Senior ministers are poised to meet as soon as a deal is ready to be signed off, with speculation mounting over a special Cabinet meeting as early as this weekend.
But a senior UK Government source said reports circulating that an agreement could come within this timeframe should be taken with a “very large pinch of salt”.
Michael Barnier, the EU’s chief negotiator, and Brexit Secretary Dominic Raab could meet in the next few days to seal an agreement, Austria’s Der Standard newspaper reported.
This would pave the way for a special summit of EU leaders in Brussels on November 25.
And asked about the prospects of a breakthrough in the coming week, Mr Tusk told Channel 4 News: “I hope so … but still we need maybe five, maybe six, maybe seven days.”
A Downing Street source stressed that no agreement had yet been reached and no Cabinet meeting scheduled. “We are still in negotiations, and on that basis we don’t know when and if this will conclude,” he said.
Mr Coveney told the Irish Canada Business Association conference in Dublin: “I would urge caution that an imminent breakthrough is not necessarily to be taken for granted, not by a long shot.
“Repeatedly people seem to make the same mistake over and over again, assuming that if the British Cabinet agrees something, well, then that’s it then, everything is agreed.
“This is a negotiation and needs to be an agreement of course between the British Government, but also with the European Union and the 27 countries that are represented by Michel Barnier and his negotiating team.
“So while of course we want progress to be made and we want it to be made as quickly as possible because time is moving on, I would urge caution that people don’t get carried away on the back of rumour in the coming days.”
Theresa May last month told MPs that 95 per cent of the deal had been agreed, although the key sticking point of the “backstop” to prevent a hard border between Ireland and Northern Ireland remained unresolved.
The Prime Minister’s plan would see the whole UK effectively agree to remain in the customs union to help avoid a hard border with Ireland as a backstop if no other arrangement can be found.
Brexiteer MPs, including Environment Secretary Michael Gove, have called on Mrs May to release full legal advice setting out how the arrangement could be ended to avoid it becoming a permanent settlement.