The Argentine forward committed his future to the Italian club.
Speaking to www.tuttomercatoweb.com, the Argentine striker said that although he was flattered by the speculation, he has no intention of leaving Serie A to play for the Primera Division champions.
"Atletico Madrid's interest? They are a big club that has done really well with Diego Simeone," the 21-year-old said. "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 was rumoured to be Atletico manager Diego Simeone's number-one choice to replace star striker Diego Costa after the Brazilian moved to Chelsea this summer.
Icardi missed long stretches of last season through injury, but scored nine goals in his 22 appearances in Serie A. Inter finished fifth in the league and will play in the Europa League next season, and the Argentina international is looking for both he and the club to kick on next year.
"It was a hard year for me and for the club," he 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."