It is the first time the British side has put a figure even unofficially on the so-called divorce bill, one of the biggest sticking points in the Brexit negotiations.
However, it falls well short of the 100-billion-euro ($118 billion) sum discussed in Brussels.
The newspaper report, based on unnamed government sources, said Britain would pay this only if the EU agrees to negotiate the financial settlement as part of a future trade deal.
Brussels has said progress must be made on the divorce bill, as well as the rights of European citizens living in Britain and the Irish border issue, before any talks can start on a free trade agreement.
EU Brexit negotiator Michel Barnier has warned that the trade negotiations, which Britain hopes will start in October, may be pushed back to December because Britain is stalling on the bill, diplomats said last month.
British officials are looking at proposing a transition deal where Britain would continue to make net payments to the EU of 10 billion euros a year for up to three years after it leaves in March 2019, the Telegraph said.
- 'International obligations' -
This money, paid in return for continued access to Europe's single market, would be a "partial down-payment" on the final bill.
Prime Minister Theresa May's government refused to comment Sunday on "speculation", although a source told AFP that Britain "will meet our international obligations, but not pay more than we need to".
But he said the "methodology" for determining how much Britain must pay should be worked out during the first phase of the Brexit negotiations -- which is due to end in October, before trade talks begin.
A number of senior EU officials have previously confirmed to AFP the estimate of 100 billion euros -- a figure British ministers have rejected as "ridiculous".
EU officials have also said the total figure may eventually come down because of jointly-held assets that the EU must reimburse Britain for. One earlier estimate put the figure at 60 billion euros.
After the referendum vote for Brexit last year, London began the two-year process of ending its membership of the EU in March.
Formal negotiations with the EU began in June, with the next round of talks between Barnier and British Brexit Secretary David Davis due to resume in Brussels on August 28.
EU leaders meeting at a summit in October must agree there has been "sufficient progress" in the early talks before agreeing to move onto trade negotiations.
Britain is keen to agree a new free trade agreement to replace its membership of Europe's single market, which May wants to leave in order to end free movement of workers into Britain from the rest of the EU.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)