The government has previously promised a referendum in 2027, but it is now expected to be brought forward. Membership negotiations were frozen in 2013 by a previous government.
The date for the vote is expected to be announced in the coming weeks, according to the sources.
The advance comes after visits by a number of EU politicians to Iceland and by Icelandic politicians to Brussels.
According to one of the sources, Iceland could become an EU member before the other current candidate countries.
