But the revelation risks enraging Brexiteer backbenchers and will fuel fears that Britain will send huge amounts of money into the EU's budget which the public may never about.
A senior EU official told the Sunday Times: "A deal is now doable. This is a breakthrough.
"The Brits will list categories in which they want to honour their commitments. They will present different calculations than the Commission, but for us it's all about accepting the principle — not about having a specific figure.
"The withdrawal agreement will not contain a figure — the Brits only need to indicate what, and how. Not how much.
"It will all be about the presentation in order to help May and her cabinet deal with the political sensitivities. But the stars are aligned for a successful deal.
"We are in the business of securing an agreement. We need to improve the atmosphere in order to move on to the real difficult bit — the trade deal."
It comes after the EU finally indicated it is ready to start talks on a post-Brexit trade after weeks of stalemate.
Donald Tusk, president of the European Commission, suggested on Friday it was "possible" talks on trade could begin at a crunch summit of EU leaders in Brussels next month.
But he warned of a "huge challenge" ahead – and set the Prime Minister a new deadline of ten days for progress on 'all issues' before trade negotiations start.
It comes after Mrs May secured agreement from her Cabinet this week to increase the Government's offer on the Brexit "divorce bill".
The EU has so far refused to start trade talks until sufficient progress is made on the Brexit bill, EU citizens rights and the Irish border.
May got her Cabinet to sign off on doubling the Brexit bill to £40b but only on condition of getting a trade deal.