Argentine Icardi, 21, has made a positive start to the season, scoring three goals in his opening six games, leading to calls for Inter to tie him down to a new contract.
While the former Sampdoria man says there has been no talk of a new deal thus far, he assured Inter fans he wants to stay at San Siro.
"On the renewal I don't know anything yet. But I chose Inter, and I want to stay here," Icardi told the Gazzetta dello Sport.
"I want to stay because here we have a desire to build something, because Milan is a great city, because the President (Erik Thohir) has very clear ideas and because I want to stay here."
The Nerazzurri have struggled of late, suffering back-to-back defeats to Cagliari and Fiorentina to leave them 10th in Serie A.
During the 4-1 home loss to the former, the San Siro crowd showed their frustration by whistling head coach Walter Mazzarri.
"We need the help of the San Siro crowd," added Icardi. "Don't whistle, instead cheer for the team and for the Coach.
"Against Napoli (who Inter face at home this Saturday) I'm convinced we'll have support for 90 minutes.
"This is a new team, and a young one. Winning will take time, but that's what we all want to do.
"Three reasons to believe in Inter? One: because I like this squad and the work the club is doing.
"Two: because there are many young players with a desire to win, because they haven't won anything before.
"Three: we are a united squad, on and off the field."