A deal giving London, the world's largest centre of international finance, basic access to European Union financial markets after Brexit is nearly done, a British official said.
Such a deal would give the United Kingdom a level of access to the EU similar to that of major U.S. and Japanese firms, while however tying it to many EU finance rules for years to come.
"We are making progress," the official, who spoke on condition of anonymity, told Reuters.
But the official said the financial services deal would be based around the EU's existing "equivalence" system - far short of the deep and preferential post-Brexit market access that many have been hoping for.
Another British official also speaking on condition of anonymity said that, while there was progress, nothing was finalised yet.
However, European Union negotiator Michel Barnier took tweeted on Thursday that the press article on Brexit and financial service was "misleading."
The financial services deal was part of the overall Brexit deal that Prime Minister Theresa May hopes to strike by the end of the year at the latest, the second official said.
Britain's Brexit ministry said progress was being made on reaching a financial services deal, while the European Commission had no immediate comment.
Many top bankers fear that Brexit will slowly undermine London's pre-eminent position as the world's biggest international financial centre, and a Reuters survey found that, so far, just over 600 are moving away.
Global banks have already reorganised some operations ahead of Britain's departure from the European Union, due on March 29.
The Times newspaper reported that a tentative deal had been reached on all aspects of a future partnership on services, as well as the exchange of data.
The pound jumped following the report in The Times, extending gains in early trade to reach $1.2914 by 0855 GMT.
Britain is currently home to the world's largest number of banks and hosts the largest commercial insurance market.
About six trillion euros ($6.82 trillion) or 37 percent, of Europe's financial assets are managed in the UK capital, almost twice the amount of its nearest rival, Paris.
In addition, London dominates Europe's 5.2 trillion euro investment banking industry. While New York is by some measures bigger, it is more centred on American markets.
Since Britain voted to leave the EU more than two years ago, some of the world's most powerful finance companies in London have been searching for a way to preserve the existing cross-border flow of trading after Brexit.
The tentative deal being discussed falls far short of that.
Currently, inside the EU, banks and insurers in Britain enjoy unfettered access to customers across the bloc in all financial activities.
Equivalence, however, covers a more limited range of business and excludes major activities such as commercial bank lending. Law firm Hogan Lovells has estimated that equivalence rules cover just a quarter of all EU cross-border financial services business.
Supporters of Brexit had hoped that leaving the EU would allow them to dispense with EU rules on financial services such as caps on bankers' bonuses to turbo-charge London as a financial hub.
Britain's Financial Conduct Authority said on Wednesday that UK financial rules should stay aligned with those in the EU after Brexit, a basic condition for Brussels to grant equivalence.
Faced with having Europe's biggest financial centre on its doorstep, the EU has begun tightening conditions for equivalence in areas such as clearing derivatives and investment banking.
Under the current system, Brussels can scrap an equivalence designation within 30 days in some cases - a step it has never taken - and Britain has called for a far longer notice period.
The Times reported that neither side would unilaterally deny market access without first going through independent arbitration and providing a notice period significantly longer than 30 days.
Britain on Wednesday said there was no set date for Brexit talks to finish, backtracking from a letter by Brexit minister Dominic Raab that suggested a deal on the terms of its departure could be finalised by Nov. 21.