The U.K. and the Netherlands will propose to Iceland a new plan to reimburse the countries for their multibillion-dollar bailout of the Icelandic banking sector, a person familiar with the matter said.

If the plan is accepted, Iceland wouldn't have to put debt repayments to a referendum—a step that has thrown into question the international plan to bail out the country and cast doubts on its bid to join the European Union.

In January, Iceland's president vetoed a bill to reimburse the U.K. and the Netherlands for bailing out their countries' depositors in Icelandic accounts. The matter is set to go to a referendum.

On Friday, the main details of the repayment remained the same: Iceland would pay about $5 billion to the U.K. and Netherlands but can take advantage of a seven-year grace period before payments must begin. Under the new proposed terms, the U.K. and Netherlands would change the interest payments from a fixed to a floating rate—a move they believe will ease Iceland's burden, this person said.

The October 2008 collapse of one bank, Landsbanki Islands, triggered the trouble. Hundreds of thousands of British and Dutch depositors, wooed by high interest rates, had placed money with Landsbanki through an Internet arm called Icesave.