The UK may be prepared to give up 12% to 15% of its annual £3.8bn EU rebate to reach a deal on budget reform.
Prime Minister Tony Blair denied Tory claims this amounted to "surrender".
Mr Blair wants to reduce the overall EU budget and slim down payments to new members, while making sure the UK pays a "fair share" towards enlargement.
He said the bulk of the annual refund would not be renegotiated without reform of farming subsidies. However, new EU states have reacted coolly.
They object to part of the plan which would see a cut in their development aid, but the UK says other measures would compensate.
The last attempt to agree a framework budget for 2007-13, which will climax at a summit in Brussels on 15 and 16 December, ended in failure in June.
The UK then rejected calls to give up its rebate without an overhaul of the Common Agricultural Policy, but this faced fierce opposition from France and others.
BBC Europe editor Mark Mardell said Mr Blair has now indicated he is prepared to give up what the new EU countries pay towards the British rebate, but will not move on the money paid by the 14 old member states.
The prime minister was under pressure "simply to do a deal" on the budget during his EU presidency which is due to end on 1 January, said our correspondent.
Mr Blair said the UK was willing to pay its fair share of EU funding, but called for "fundamental reform".
He is proposing a mid-term review of the budget, which would allow for a change in spending priorities in the second half of the 2007-13 period.
Speaking after talks with central European leaders in Budapest, Mr Blair said it would not get any easier to reach a deal in 2006.
New member states gave a mixed response to the plans to cut 10% from development aid they were due to receive.
Poland's prime minister suggested some progress was being made towards a deal.
Hungary's prime minister warned that countries were "still far from agreement" on the proposal, which Estonia had earlier branded "unacceptable".
Conservative leader Michael Howard said UK taxpayers would be "saddled" with more EU costs, while getting nothing in return.
He said fundamental reform of the budget could have been achieved "but we squandered a tremendous opportunity."
'Can of worms'
Nigel Farage, leader of the UK Independence Party in the European Parliament, said Mr Blair had alienated all 24 other nations in the budget process.
"At the same time he's opened a can of worms in this country, because we haven't discussed Britain's contribution to the EU properly for over 20 years.
"And suddenly British taxpayers are going to say why should I, in a couple of years time, pay 5p in the pound of my income tax straight to a European Union that hasn't had its accounts signed off for the last 11 years?"
Liberal Democrat Treasury spokesman Vince Cable said: "There's a danger of getting the worst of all possible worlds.
"Britain gives up £1bn a year, the Eastern European countries get less money and there is no agreement to reform agriculture."