Boris Johnson and President Ursula von der Leyen of the European Commission are scheduled to meet at lunch today to take stock of the progress of the negotiations, but both sides have maintained that the most probable outcome remains a no-deal exit.
Negotiations continued late on Saturday night in the midst of ongoing disputes over so-called level playing field arrangements governing the level of state assistance that governments should offer to their nation's businesses.
The EU argued that allowing the United Kingdom to have complete control over state aid laws would give British companies an unfair advantage if they continued to have access to the single market of the bloc, however, the United Kingdom believed that it would be an unreasonable loss of power to remain bound by EU regulations.
Both sides have indicated that other unresolved problems, including fishing rights and the role of the European Court of Justice in resolving trade conflicts between the United Kingdom and the EU, would have to be resolved by the deadline of tonight if there were any hope of an agreement being struck.
But speaking on Saturday evening, the government source said The talks continue overnight, but the EU's offer on the table remains unacceptable as things stand."
"The Prime Minister will leave no stone unturned in this process, but he is absolutely clear: any agreement must be fair and respect the fundamental position that the UK will be a sovereign nation in three weeks' time."
Foreign Secretary Dominic Raab said that over the weekend, the UK team had been working incredibly hard" but maintained that the UK would not support an arrangement that left it bound by EU law.
Speaking to Sky's Sophy Ridge on Sunday, Mr. Raab said the United Kingdom "wants to be treated like any other independent and self-respecting democracy" and said the EU was "concerned that actually, Britain might do rather well once we leave"
The senior cabinet minister also indicated that he "can't close the door" on talks extending beyond the deadline for tonight if the "political logjam" could be resolved by talks between Mr. Johnson and Ms von der Leyen.
"That can only happen at the political level of the prime minister and Commissioner Von der Leyen," he said.
"If we're 99 percent there on the outstanding issues, you wouldn't want to leave any stone unturned, but I think it's quite a high bar."
With negotiations going down to the wire, in the event of a no-deal departure, ministers have encouraged retailers to begin stockpiling food.
Ministers and supermarket bosses are worried that the chaos caused by a cliff-edge exit could lead to food shortages in the new year according to The Sunday Times.
One senior advisor to a big retailer told the paper: "A week ago when ministers said to prepare for no-deal, there was a conversation. The message this weekend is that it's no-deal."
Ministers and supermarkets are highly worried about panic-buying. When people began to stockpile toilet rolls, they saw what happened over Covid and realized how easy it can go wrong.
"That will be nothing compared to what will happen. Meat supplies will be fine and fruit comes from South America but there are likely to be shortages of vegetables for three months."
In the meantime, ministers announced on Sunday that four Royal Navy patrol vessels had been placed on standby as of 1 January to defend British fishing waters if no agreement existed.
The 80-meter armed craft will be used to prevent French fishing vessels from accessing the coastal waters of the United Kingdom, with the power to intercept and search boats that they believed were illegally fishing.
But the proposals have come under fire, including from senior Tory MP Tobias Ellwood, who said it would be "undignified" to send military ships.
He told the BBC's Today show, "This isn't Elizabethan times anymore, this is global Britain - we need to be raising the bar much higher than this,"
"Being ready for the worst-case scenario and using this final 48 hours to actually get a deal, they are two very different things."
Spanish Foreign Minister Arancha Gonzalez said the move by Mr. Johnson was for the gallery" in response to the news.