The EU's chief Brexit negotiator Michel Barnier has arrived in London for another round of Brexit talks with his UK counterpart David Frost.
Before he arrived in the British capital, he told a meeting of EU envoys: "We are not far from the take-it-or-leave-it moment."
He also tweeted the message, that the "same significant divergences persist."
In-person talks were paused last week after one of the EU's negotiating team tested positive for coronavirus, but they were set to resume in London on Saturday.
The window for an agreement on future trade relations is fast closing.
Failure to achieve one by January 1, when the UK's Brexit transition period ends, will have heavy economic consequences for both sides.
Britain's chief negotiator Frost was similarly cautious about the chances of a breakthrough.
In a tweet, he wrote: "Some people are asking me why we are still talking. My answer is that it's my job to do my utmost to see if the conditions for a deal exist.
"It is late, but a deal is still possible, and I will continue to talk until it's clear that it isn’t."
In London, British Prime Minister Boris Johnson said it was up to the Europeans to make a move and claimed that Britain was prepared in the event that talks collapsed.
The "likelihood of a deal is very much determined by our friends and partners in the EU," he told reporters.
Negotiations have been deadlocked for months over the issues of fishing rights, the governance of a deal, and the “level playing field” conditions aimed at preventing unfair competition by cutting standards or increasing state subsidies.