The EUs chief negotiator has reportedly proposed extending the transition period as a Tory rebellion over Mrs Mays draft withdrawal agreement raises the spectre of no-deal.
The transition period is scheduled to start on March 29 next year and end on December 31, 2020, under the proposed Brexit deal announced by the Prime Minister last week.
But in a note to Brussels diplomats, Bariner has suggested the transition period could be extended for another two years – a scenario likely to infuriate Brexit-supporting MPs.
During the proposed extended transition period Britain may have to abide by free of movement rules and continue paying large sums to the EU budget.
Extending the transition period could allow negotiators from London and Brussels to strike a deal more politically acceptable to both Remain and Leave-supporting MPs in Westminster.
Mrs Mays deal faces the prospect of being voted down in the House of Commons given the fierce opposition to her withdrawal plan puts a majority in doubt.
POSTPONEMENT: Brexit could be delayed for another two years under reported EU proposals (Pic: GETTY)
More time could mean a comprehensive trade deal is struck that avoids the need for a backstop plan for Northern Ireland – a point of major contention for Brexiteers.
In his reported communique, Mr Barnier is said to have noted that the political situation in Westminster is "volatile".
Speaking at a press conference this morning, Barnier said the draft Brexit deal reached between the bloc and London was "fair and balanced" but admitted an extension to the transition period was possible.
Barnier told a news conference after briefing 27 national EU ministers that they in general approved of the draft divorce agreement reached last week.</span></span>
“The deal is fair and balanced”
"We are in fact at a decisive moment in this process, no one should lose sight of the progress that has been achieved in Brussels and in London," Barnier said.
"Globally speaking, the deal is fair and balanced.
"In particular, member states support the draft withdrawal agreement. The EU side will still have to decide the internal process for agreeing to extend the transition period."</span></span>
FAIR AND BALANCED: Barnier said the withdrawal agreement has been accepted by EU leaders (Pic: GETTY)
Any extension to the transition period would be mutually agreed between the UK and the EU.
Back in Westminster, Brexiteers could view extending the period as a concession to Brussels.</span></span>
Mrs May is already facing the prospect of a no-confidence vote as Tory Brexiteers have almost reached the threshold of letters required to trigger the process.
Business secretary Greg Clark told the BBC that extending the transition period could be an option the government considers.
Asked on BBC radio about an extension to the transition period, Clark said: "It would be at our request."
"It would be our discretion, it would be purely for us if we wanted to and there are reasons we may not want to take that up, it would be available to us," he said.
STANDING FIRM: Theresa May has vowed to 'see it through' as she faces a rebellion (Pic: SKY NEWS)
He did not rule out a suggestion that it could last until 2022.
"If we were six weeks away from concluding a future economic partnership and agreeing that then it may make sense to extend the transition period," Clark said.
But former president of the European Council Herman Van Rompuy said there was little prospect of altering the Brexit deal at this stage, telling the BBC: "On the main parameters what I hear is that there is almost no room for manoeuvre."
Mr Van Rompuy rejected claims that the EU had bullied the UK, stating: "You agree or you don't agree. We agreed and that is nothing to do with bullying or something else."</span></span>