The whopping sum money would come on top of the £18 billion the Prime Minister already promised to pay Brussels to secure a transitional deal in her Florence speech in September.
And the offer would allegedly be made ahead of a crunch Brussels summit in December, when leaders of the remaining 27 EU states will decide whether the UK can move on to the second phase of Brexit negotiations.
If confirmed, the £20 billion figure would bring the total to around £38 billion the total sum Britain is prepared to pay to settle its liabilities –
But the figure would still be well short of the £53 billion sought by Brussels.
The EU’s chief negotiator Michel Barnier last week slapped a 14-day deadline on Britain to outline what they are prepared to pay towards the contested exit bill.
But Ministers and MPs now expect Downing Street to simply ignore that enforced time limit and instead set out plans early next month.
Mrs May has so far held back from putting any figure on the financial settlement in public, and it is thought likely that any offer ahead of the December 14 to 15 summit would come in the form of clearer guidance on what commitments the UK is ready to cover.
The Prime Minister’s official spokesman said reports of a £20 billion figure were “yet more speculation”.
And Brexit Department sources insisted that no final decision had been made about whether an offer would be made.
A Government spokesman added: “As we have always said, the financial settlement will only be resolved in the context of our future relationship”.
On Sunday Brexit boss David Davis insisted that taxpayers would not “want me to just come along and give away billions of pounds.”
He added: “So we are being very, very careful and it’s taking time, and we will take our time to get to the right answer.”
But the source also declined to confirm suggestions from senior MEP Manfred Weber – a close ally of German Chancellor Angela Merkel – that Mrs May had indicated a readiness to compromise in a meeting on Wednesday.
Following their talks at 10 Downing Street, Mr Weber, who leads the centre-right EPP in the European Parliament, told reporters: “I am more optimistic. There is progress and a will to see progress.”
On the financial settlement, Mr Weber said that while the UK did not have to state a figure at this stage, it did need spell out which of its outstanding commitments to the EU it was prepared to honour.
Mrs May’s spokesman described the meeting as “constructive”, adding: “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.”
Failure to secure agreement at the December summit would be a major setback for the Prime Minister as the next opportunity for EU leaders to green light the second phase talks will not be until March.
It would almost certainly prompt demands from hardline Brexiteers for Mrs May to walk away from the negotiating table.
Shadow chancellor John McDonnell told Sky News: “Our problem is this – we do not know from one day to another what the Government’s strategy is or which coalition there is in the Cabinet that is actually ruling the roost at the moment.
“In that way, there’s an inconsistent approach. We have a Government in disarray. There’s no way you can negotiate a decent deal when really the Government that’s meant to be doing these negotiations is directionless.”
Brexit Secretary David Davis is due to make a keynote speech on Brexit to an economic summit in Berlin on Thursday evening.