Iceland wants a new deal to avoid a referendum on March 6 on a previous agreement, which the island's citizens are almost certain to reject, undermining the government's credibility and delaying access to vital economic aid.
Talks on resolving the Icesave dispute appeared to have collapsed last week, but Icelandic media, citing unnamed sources, said officials from Britain and Iceland met in London and that further meetings were planned over the weekend.
British and Icelandic officials were not immediately available to comment on the reports.
Icelandic daily Morgunbladid and Icelandic television said the Dutch, who like Britain reimbursed savers who lost deposits in Icesave accounts, were not at the meeting, but could go along with a deal if Iceland and Britain reach one.
The Dutch government collapsed last week and the country has a caretaker administration until elections in June.
On Friday, Iceland's finance minister said that there was no point in further meetings, explaining the three countries were divided over what interest Iceland should pay on the debt.
However, Icelandic Prime Minister Johanna Sigurdardottir held out the possibility of a last-minute deal that would make the referendum unnecessary.
Iceland desperately needs to solve the Icesave impasse in order to get international aid flowing to its economy, which contracted around 7.7 percent last year and is expected to shrink again in 2010.
The International Monetary Fund and Nordic countries have promised to loan Iceland around $4.5 billion to help it kickstart the economy. But after initial payments, much of the cash is frozen pending resolution of the Icesave debt.
The government and opposition agreed to a deal with the UK and the Dutch last year, but the repayment terms are seen as harsh by many Icelanders and the country's president refused to sign the deal into law, triggering the referendum.
The Icesave debt amounts to more than $15,000 for every one of Iceland's 320,000 people, though most of the money is likely to be covered by the sale of the assets of the bank which offered the Icesave accounts.
A new offer by Britain and the Netherlands of easier payment terms for Iceland was rejected by Reykjavik last week.
If no solution to the issue is found, Iceland risks defaulting on its foreign debt, the bulk of which falls due in 2011, further extending its exclusion from overseas financial markets and prolonging the current recession.