The European Union has floated a figure of 60 billion euros and wants significant progress on settling Britain's liabilities before talks can start on complex issues such as future trading arrangements, Reuters reported.
The government department responsible for Brexit talks declined to comment on the Sunday Telegraph article. So far, Britain has given no official indication of how much it would be willing to pay.
The newspaper said British officials were likely to offer to pay 10 billion euros a year for three years after leaving the EU in March 2019, then finalize the total alongside detailed trade talks.
Payments would only be made as part of a deal that included a trade agreement, the newspaper added.
"We know (the EU's) position is 60 billion euros, but the actual bottom line is 50 billion euros. Ours is closer to 30 billion euros but the actual landing zone is 40 billion euros, even if the public and politicians are not all there yet," the newspaper quoted one "senior Whitehall source" as saying.
Whitehall is the London district where British civil servants and ministers are based.
A second Whitehall source said Britain's bottom line was "30 billion euros to 40 billion euros" and a third source said Prime Minister Theresa May was willing to pay "north of 30 billion euros", the Sunday Telegraph reported.
David Davis, the British minister in charge of Brexit talks, said on July 20 that Britain would honor its obligations to the EU but declined to confirm that Brexit would require net payments.
British foreign secretary Boris Johnson, a leading Brexit advocate, said last month the EU could "go whistle" if it made "extortionate" demands for payment.
Last week the Bank of England said Brexit uncertainty was weighing on the economy. Finance minister Philip Hammond wants to avoid unsettling businesses further.
If Britain cannot conclude an exit deal, trade relations would be governed by World Trade Organization rules, which would allow both parties to impose tariffs and customs checks and leave many other issues unsettled.
The EU has also wants agreement by October on rights of EU citizens already in Britain, and on border controls between the Irish Republic and the British province of Northern Ireland, before trade and other issues are discussed.