Icardi, 25, has been one of Serie A's most prolific scorers in recent years, having scored at least 20 league goals in three of the previous four seasons.
Icardi reportedly has a €110 million (£97m/$126m) release clause valid for foreign clubs, further clouding his outlook.
However, the Argentina international has now revealed his happiness with Inter, admitting he has had interest from other sides, but his desire to play in the Champions League with the club he joined in 2013 convinced him to remain.
"I'm happy to stay here," Icardi, who's current deal expires in 2021, told Sky Italia.
"There have been contacts, but I decided to stay here for myself and my family. I had the dream of playing in the Champions League in the Inter shirt and therefore I couldn't leave."
Icardi also confirmed that he hoped to sign a new contract with the club, though he was uncertain if it would be completed prior to the holiday season.
"We will try to find a renewal, but I don't know if it will arrive before Christmas."
Icardi has returned from international duty with Argentina, where he started in their 1-0 loss to Brazil.
He and Inter will face a busy eight-day stretch starting Sunday when they battle local rivals Milan, then a midweek a Champions League date away to Barcelona and a Serie A matchup against Lazio the following Monday.