The German Chancellor is said to be worried the Prime Minister will emerge dramatically weakened by Brussels’ sky-high demands which could lead to a hard Brexit.

EU chiefs are demanding Britain hands over a huge divorce bill payment plus guarantees on EU citizens’ rights and the Irish border before agreeing to discuss future trade.

It leaves Mrs May under huge pressure as she tries to balance the goal of moving talks forward at the EU’s December summit with Tory voices calling for the payment to be minimal.

A source close to Mrs Merkel told Bloomberg the German leader was seriously worried Mrs May could be deposed as leader if the bloc’s demands are too high.

And Mrs Merkel allegedly fears the EU's tactics could see Mrs May replaced as Prime Minister by a hard Brexit-backing Tory, leaving a nightmare scenario for Brussels.

Downing Street today dismissed reports Mrs May is ready to offer another £20 billion in Brexit payments to break the deadlock.

The Sun reported the offer would be made ahead of a crunch Brussels summit in December, when leaders of the remaining 27 EU states will decide whether sufficient progress has been made on the UK's financial obligations.

And that figure would bring to around £38 billion the total sum Britain is prepared to pay to settle its liabilities - still short of the £53 billion Brussels is demanding.

The Prime Minister's official spokesman said reports of the new figure were "yet more speculation".

And he declined to confirm suggestions from senior MEP and close Merkel ally Manfred Weber that Mrs May had indicated a readiness to compromise in a meeting on Wednesday.

Following their talks at 10 Downing Street yesterday, Mr Weber, who leads the centre-right EPP in the European Parliament, said the situation was improving.

He said: "I am more optimistic. There is progress and a will to see progress.

"The atmosphere is positive but we need clear and concrete commitments to step into the second phase. For now the green light is not there."

On the financial settlement, Mr Weber said, while the UK did not have to state a figure now, it had to spell out which outstanding financial commitments it was prepared to honour.

He said: "For the so-called sufficient progress question for the December council, the most important thing is not the figure. 

“The most important thing is to clarify the commitments - the areas where Great Britain has to see its commitments.”

Mrs May's spokesman described the meeting as “constructive”.

He said: "The Prime Minister set out her determination to secure a unique deal for Britain, but one that works in both our interests. 

“She also set out a very clear position in terms of an implementation period that will serve both Britain and the EU, providing clarity for business and others."

It comes as Brexit Secretary David Davis is to make a keynote speech in Germany amid hopes of a breakthrough in talks. 

Mr Davis's address, to an economic summit in Berlin, comes after the EU chief negotiator Michel Barnier warned on Friday that progress was needed within two weeks if the talks were to move to the second phase before the end of the year.