"I would have loved to have a political plan along with a military plan on how to administrate Mosul," Barzani said in an interview with CNN.
The president noted there should be a new form of governance for Mosul, whose residents belong to different religious and ethnic minorities.
"We are looking for a good solution," Barzani underscored.
On Monday, the Iraqi troops, aided by the US-led coalition, began their campaign to retake Mosul from Daesh, which seized the city in June 2014.
Barzani pointed out that the Kurds have establishes a joint committee with Baghdad to deal with potential problems during the offensive on the city and coordinate the Kurdish Peshmerga and Iraqi Security Forces.
The Islamic State, also known as Daesh in Arabic, is outlawed in many countries.