It withdrew its last bid in 2015...
The question of EU membership has become central to Iceland's attempts to form a government following October's snap election.
The Independence Party - who are euroskeptics and right-leaning - are in talks to form a difficult coalition with the liberal Reform Party and Bright Future.
AFP says that Óttarr Proppé, Bright Future’s leader, revealed that the possibility of a referendum on seeking EU membership has become an important component of these negotiations.
Actor/musician come politician Óttarr Proppé
Reform leader Benedikt Johannesson said, "We have crossed the biggest obstacles. Now we will use the next days to write the government’s policy." All parties are reported to have agreed terms on fisheries and agriculture policies - two contentious issues in Iceland.
Trawler docked in the harbor of Isafjordur, Iceland / PA
The state applied to join the EU in 2009 - but the bid was abandoned in 2015 as the country's then-foreign minister decided that joining the Union would be against Iceland's best interests as the country feared that tight fishing quotas would hurt its economy.
It is a member of the European Economic Area and the Schengen zone.
If it did want to join the EU, the earliest that it could do so would be 2022.
The country's previous PM Sigmundur Davíð Gunnlaugsson was forced to resign when his involvement with off shore accounts was revealed in the Panama Papers.