They fear Britain being locked permanently into a customs union with the EU, which would limit the U.K.'s ability to strike new trade deals around the world.
Britain leaves the EU on March 29, but a deal must be sealed in the coming weeks to leave enough time for the U.K. Parliament and European Parliament to sign off on it. Meanwhile the EU's chief negotiator, Michel Barnier, told reporters in Slovakia that "we are not there yet".
It comes after the PM last month told MPs that 95% of the deal had been agreed, with the key sticking point of the "backstop" to prevent a hard border between Ireland and Northern Ireland remaining unresolved.
DUP leader Arlene Foster said the Prime Minister appeared "wedded to the idea of a border down the Irish Sea" despite Downing Street's assurances to the contrary.
"We're going through crucial days now".
Tusk's comments came on the same day Austrian newspapers reported that Brexit Secretary Dominic Raab and European Union chief negotiator Michel Barnier could meet over the next few days to seal an agreement. Rumours are swirling that one might take place by the end of November, weeks ahead of a pre-planned European Union summit in mid-December, but Barnier declined to say when or if that would happen.
"Seven days is probably pushing it, but I am optimistic that there will be a Brexit deal", Hunt said, adding it is "very, very hard to resolve but I am confident that we can".
Speaking to a conference of the centre-right European People's Party (EPP) in Finland, Mr Barnier said: "The European project is fragile, it is under threat, it is perishable and at the same time it is vital".
European Commission President Jean-Claude Juncker said that British Prime Minister Theresa May "is, as we are, made a decision to have the deal, and we will have a deal".
Farage, the former leader of the UK Independence Party, was one of the most high-profile figures in the successful campaign to convince British voters to quit the bloc.
Brexit is expected to dominate the agenda of the British Irish Council, which also involves the first ministers of Scotland and Wales, Nicola Sturgeon and Carwyn Jones.
Health Secretary Matt Hancock said that, while the Attorney General's legal advice to government is considered confidential, he could answer MP's questions about it.