It is the first time the British side has put a figure on its so-called Brexit bill - although the sum falls well short of the €100 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 settlement as part of a deal on future relations, including trade.
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.
British officials are looking at proposing a transition deal where Britain would continue to make net payments to the EU of €10 billion a year for up to three years after it leaves in March 2019, the Telegraph said.
This money, paid in return for continued access to Europe's single market, would be a "partial down-payment" on the final bill.
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The EU's chief negotiator, Michel Barnier, has declined to publicly name a sum for Britain's divorce bill, which includes its share of EU spending projects already agreed, as well as pension contributions of staff, among other expenses.
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.
A number of senior EU officials have confirmed to AFP the estimate of €100 billion.
Officials have previously said there is scope for paying the bill in instalments, and that the total figure may eventually come down because of jointly-held assets that the EU must reimburse Britain for.
