At a special meeting with ambassadors from the EU’s 27 member states, Barnier floated the prospect of extending the Brexit transition until the end of 2022.
His idea would allow an extra two years to negotiate a trading relationship, but means the UK would continue to follow EU rules and pay into its budget with no say for six and a half years after the 2016 vote to leave.
Both sides have already agreed a transition period of 21 months, until the end of 2020, as well as the chance to extend once by mutual consent. The length of the extension is still to be finalised by negotiators.
The transition period, which the British government prefers to call the implementation period, would see the UK following all EU laws and European Court of Justice rulings, while having no ministers or MEPs in the EU decision-making process.
Theresa May has previously suggested an extension of only a few months would be needed, but the EU is still waiting on the UK to make a formal proposal.
Negotiations between the EU and UK were continuing on Sunday as Brexit talks entered a critical final week, ahead of a special summit on 25 November when both sides hope to seal the deal.
While Westminster remains in political turmoil, with leading Brexiters angling to send the prime minister back to Brussels to renegotiate the 585-page withdrawal treaty, the EU regards the text as finalised.
European leaders have zero appetite to reopen talks, despite some unhappiness about the customs union being offered to the UK as an insurance plan to avoid a hard border on the island of Ireland. “While certain member states would certainly like to see more, they have to swallow it for now,” one diplomat said.
The ambassadors did not discuss the cost of a transition extension – the UK’s net contribution to the EU budget was £9.6 billion (US$12.3 billion) in 2016, but would have been £14.5 billion without the rebate.
The EU has previously said the UK would no longer be entitled to the rebate after 2020.
At the meeting, Spain voiced unhappiness about the status of Gibraltar, but EU sources were not expecting Madrid to stand in the way of an agreement.
Spain has publicly welcomed the deal on Gibraltar, but its minority government is under pressure from opposition parties over the status of the dependency.
Instead, EU member states are focusing their attention on the statement on future relations, a political declaration that is expected to be released on Tuesday.
France is taking a strict approach to avoid any watering down of the EU’s four freedoms, while economically liberal countries, such as the Netherlands and the Baltic states, are looking for a more ambitious text.
Ministers from EU27 will meet in Brussels on Monday to give further input into the document, which is due to be signed off at the Brexit summit next Sunday.
May said she would be travelling to Brussels to meet the European Commission president, Jean-Claude Juncker, this week, but her announcement has not been confirmed in Brussels.
“President Juncker is of course ready to meet PM May once the negotiations on the political declaration have advanced in a decisive manner,” a commission spokesman said.
“Work on this is ongoing between the negotiators,” he said, adding it was “too early to say when a meeting could take place”.