The 21-year-old has been strongly linked with Atletico as the Primera Division champions seek to strengthen their attack following the departure of David Villa this summer and Diego Costa's impending move to Chelsea.
However, Icardi, who joined Inter from Sampdoria last year, has no intention of leaving the San Siro any time soon.
"Atletico Madrid's interest? They are a big club that has done really well with (Argentinian coach Diego) Simeone," Icardi said to www.tuttomercatoweb.com. "I'm flattered but I want to remain here.
"I am here because Inter is a big club.
"Money is not important because we already have a privileged life as a footballer.
"I have four years left on my contract, I am happy here and I want to remain."
Icardi struggled with a sports hernia in the 2013-14 season and scored nine goals in 22 league appearances.
"It was a hard year for me and for the club," the once-capped Argentina international said. "Fortunately, we were able to achieve our aim to qualify for Europe this season.
"Now we start from the beginning and we hope to do well.
"I still have a lot of work to do to earn a regular spot in the team.
"In the games that I have played, I have proved my worth."
Inter, coached by Walter Mazzarri, finished fifth in Serie A and will compete in next season's Europa League.