Channel 2 television, without citing sources, said Norway was the most likely candidate for such a role. Oslo is seen as sympathetic to Iceland's plight and mediated between London and Reykjavik in the 1970s cod wars over fishing rights.
However, a spokeswoman for the Norwegian foreign ministry said Oslo had not been asked to play the role of a mediator, although it had a good dialogue with Reykjavik. No one was available for comment at the Icelandic foreign ministry.
Iceland owes the British and Dutch governments the money for losses related to the collapse of Icesave online bank accounts in late 2008, but repayment terms have yet to be settled.
Earlier this month Iceland's president refused to sign a law setting out the terms, forcing a referendum on the issue and holding up the flow of international aid which is vital for recovery in Iceland's stricken economy.
The referendum is due to be held on March 6.
Iceland's government has been examining the possibility of withdrawing the disputed Icesave bill altogether and persuading the British and Dutch governments to return to the negotiating table to hammer out a new agreement.
Britain and the Netherlands have already compensated their savers who lost money in Icelandic accounts, and they now want the money back from Reykjavik. However, the proposed settlement has faced strong public opposition in Iceland.
Britain and the Netherlands have not said they would be willing to go back to the negotiating table, and the Dutch finance minister said this week his country would not initiate any new talks over the Icesave issue.
Opinion polls indicate the Icesave bill will be rejected in the referendum. If that happens, parliament will revert to an earlier version which was rejected by the British and Dutch governments because of limits it places on repayment.
A rejection could further delay a solution to the Icesave issue, hold up a key review of Iceland's economic aid programme with the International Monetary Fund and postpone the next tranche of aid money from a group of Nordic countries.
(Reporting by Omar Valdimarsson and Nick Vinocur; writing by Nick Vinocur, editing by David Stamp)