The UK could end up paying an EU "divorce bill" of up to €55bn, prompting the threat of a Brexit backlash against Theresa May.
Officials close to the talks were reported as saying there was a broad agreement on a framework for the UK to settle liabilities expected to total around €45bn-55bn.
The reported deal was described by former UKIP leader Nigel Farage as a "sellout".
He said: "I have always argued that no deal is better than a bad deal. Make no mistake about it, €55bn to leave the EU is a very, very bad deal."
Other reports had put the figure at up to €100bn, although the Financial Times reported that the actual payment may only be around half that, with Britain pushing for a figure of between €40-45bn.
The bill includes funding for projects Britain signed up to as an EU member, loans which have yet to be repaid and pensions for European Commission civil servants.
A recent poll said just 11% of British voters would see a bill of €40bn (€45bn) or more as acceptable.
Liberal Democrat leader Vince Cable said: "If these numbers are correct, it means we're paying a heavy price to leave an institution that has benefited the country for decades."
Prominent Remain campaigner and Conservative former minister Anna Soubry said the reported deal showed "a whopping bill we must pay, price of a monumental con trick played by Leave on decent people".
Brussels officials have given Theresa May until next week to meet EU demands on a financial settlement, Irish border issues and citizens' rights before they will allow trade talks to begin.
With that deadline needed to be met for Theresa May to break the Brexit deadlock by Christmas, it has now been said UK and EU negotiators have agreed the cash part of Britain's divorce agreement.
Both The Daily Telegraph and The Financial Times said no final figure will be announced at this stage of Brexit negotiations, but reported agreement on the UK's share of EU commitments and liabilities.
A spokesman for the Department for Exiting the EU said: "Intensive talks between the UK and the European Commission continue to take place in Brussels this week as we seek to reach an agreement.
"We are exploring how we can continue to build on recent momentum in the talks so that together we can move the negotiations on to the next phase and discuss our future partnership."
In her Florence speech in September, Mrs May had outlined an initial offer of around €20bn in her attempts to break the negotiating deadlock.
Mrs May is due to meet European Commission president Jean-Claude Juncker and EU chief negotiator Michel Barnier on 4 December.
At that point, she will hope to reach a political agreement on withdrawal issues - including the financial settlement - following the continuing talks between UK and EU diplomats.
Brussels officials have warned an agreement needs to come at this stage if EU leaders are to sanction the start of the second phase of negotiations - on trade and a transition period - at a summit on 14/15 December.