The European Union is reportedly threatening to hold back Britain's final £5 billion rebate payment from Brussels as part of negotiations over the so-called Brexit "divorce" bill.
European Council president Donald Tusk has set a deadline of the start of December for Britain to make further movement on the financial settlement in order to unlock trade talks.
But according to the Telegraph, Brussels negotiators have not provided clarity on the final rebate payment for 2018, which is due to come a year in arrears after Britain's scheduled exit from the EU on March 29 2019.
The newspaper quotes "British officials" who think the rebate, first secured by Margaret Thatcher in 1984, should be "netted off" the final divorce bill.
Both the Government and the EU did not comment on the report on Friday night.
Reports, dismissed as speculation by Downing Street, have suggested Mrs May could be prepared to offer a further £20 billion in payments, which would bring to around £38 billion the total sum Britain is prepared to pay to settle its liabilities - well short of the 60 billion euro (£53 billion) sought by Brussels.
After talks with the Prime Minister in Sweden, Mr Tusk said the EU has completed the internal work necessary to give the green light for talks on trade and transition to begin at the next European Council summit in Brussels on December 14-15.
But he said that "much more progress" was needed from the UK on the divorce bill and Northern Irish border, two of the three key issues in withdrawal talks, in order to break the deadlock which has prevented the move to the second phase of negotiations which the UK is seeking.
He said he had told Mrs May that "this progress needs to happen at the beginning of December at the latest".
Mrs May told reporters as she left Gothenburg: "We are agreed that good progress has been made but there is more to be done, that we should move forwards together towards that point where sufficient progress can be declared and we can look ahead to what I have already said I want to see as a deep and comprehensive and special partnership between the UK and the remaining 27 members of the EU."
Mrs May is anxious to secure the agreement of EU leaders to open discussions on Britain's future relations with the bloc - including a free trade deal - when they meet next month in Brussels.
In meetings at the summit with Mr Tusk, Irish prime minister Leo Varadkar, Swedish PM Stefan Lofven, French president Emmanuel Macron and Italian premier Paolo Gentiloni, Mrs May came under pressure to spell out how much the UK will pay Brussels in a so-called divorce bill in order to secure progress on trade talks.
Mr Varadkar made clear that Dublin is ready to delay the start of trade talks beyond the start of next year unless the UK offers further concessions on the Northern Irish border.
After meeting Mrs May in the margins of the summit, he told reporters: "Before we move to phase two talks on trade, we want taken off the table any suggestion that there will be a physical border, a hard border, new barriers to trade on the island of Ireland.
"If we have to wait until the new year, if we have to wait for further concessions, so be it."
Brexit Secretary David Davis suggested that he wanted to see compromise from Brussels, warning EU leaders that they will get "nothing... for nothing".
"In any negotiation you want the other side to compromise," Mr Davis told the BBC. "I want them to compromise. Surprise, surprise, nothing comes for nothing in this world.
"But so far in this negotiation, we've made quite a lot of compromises. On the citizens' rights front, we've made all the running."
Asked about the Brexit Secretary's claim that the UK had made all the concessions so far in the negotiations, Mr Tusk said: "I can say only that I appreciate Mr Davis's English sense of humour."
If leaders do not agree to move to the second phase at the summit in Brussels on December 14-15, then it could mean no progress until the next scheduled European Council in March.
That would add to business uncertainty and increase the potential for the UK to leave without a Brexit deal.