The European Commission has recommended that the EU open membership talks with Iceland.
Approval is required from EU governments before talks can start.
The BBC reports a big hurdle is the lack of a deal so far to repay the Netherlands and Britain for huge debts incurred when an online bank, Icesave, collapsed in 2008.
The Icelandic krona lost about half its value in the financial crisis.
The UK and Dutch governments paid out 3.8 billion euros ($US5.4 billion) to savers who lost money when Icesave went bust.
Almost a quarter of the population signed a petition against a repayment plan, prompting President Olaf Ragnar Grimsson, to veto it last month. No deal has been reached yet on a new plan.
The commission says Iceland meets EU criteria on democracy and human rights.
But in some areas, it says, Iceland will have to make "serious efforts" to conform with EU legislation. These include fisheries; agriculture and rural development; the environment; free movement of capital; and financial services and taxation.
Iceland's government deficit rose to 14.4% of gross domestic product in 2009, and gross public debt was 130% of GDP - way above EU target levels.
The island became independent from Denmark in 1944. It has a population of 323,000.
Last July, Iceland's parliament voted to apply to join the EU. In 2008, more than 54% of Iceland's imports came from the EU and 76% of its exports went to the EU.