It's already in the Schengen.
Iceland already heavily integrated into the EU, the only outliers are currency, foreign policy, security, political institutions, customs and some trading sectors like fishing.
Currency (since the exchange rate to the Euro is what sets pricing in Iceland) and security are the reasons many want to get closer.
What do they get in security from the EU that they don't get from NATO? Is it so they can get in on the new joint EU defence funds?