Theresa May has signalled her willingness to pay the huge sum, which equates to €60 billion, via officials, the Sunday Times reported.
It is hoped that, by accepting the demand, talks can finally progress to Britain’s future relationship with the bloc in December.
The figure is around three times higher than previously offered to cover a two-year transition period.
But EU negotiators think Mrs May will hand over the money to claim a victory by starting stalled Brexit trade talks before Christmas.
And a Government source told the paper: “The value of getting a smoother process of transition and a smoother process of trade in the end game is worth quite a lot.
“These are sums that make any lubrication of the process look like small change.”
EU negotiators have called for the €60 billion bill to cover the cost of Britain’s budget commitments alongside costs of MEP pensions and aid.
But, if the offer is made, Mrs May could face fierce criticism at home for paying over the odds.
Senior figures in her own party have repeatedly urged her to walk away if Brussels demands an exorbitant divorce fee.
International Trade Secretary Liam Fox last week warned it was “unreasonable” for the EU to insist on such a high figure before trade was discussed.
He said: “We need, before we make any offer on any financial settlement, to know what we are getting in that end state,” he told the committee.
“We have said to the EU: ‘Show us what the end state looks like and we can then talk about the financial disaggregation’.
“The idea that the UK would actually agree to a sum on money before we know what the end state looks like or what any future potential would be, I think is a non-starter.
“I think it is unreasonable, given the business interests across the European Union and given the interests of international investors, not to want to start the next phase, given that I think substantial progress has been made on issues like European citizens’ rights and basic agreements on positions over Ireland.”
During her landmark Florence speech, Mrs May offered to pay £18 billion.
But the offer was immediately slapped down by Antonio Tajani, former President of the European Parliament, who said the sum was “peanuts”.