The 20-year-old forward has been the subject of intense transfer speculation, with suggestions the Argentine could leave Sampdoria in the summer.
Roberto Mancini was credited with an interest in bringing Icardi to the Etihad Stadium prior to his sacking earlier this week.
However, Manchester City will now face a serious fight to secure the player's signature, after the South American intimated he would welcome the opportunity to switch to the San Siro.
"I am glad to hear these stories," Icardi told Corriere dello Sport. "I am flattered by the Inter rumours. They are a great team with many great players from Argentina.
"San Siro is a beautiful stadium and will remain in my memory forever. I have not played there yet though. Both times I've gone there I have been on the bench."
Icardi has made 30 Serie 'A' appearances for Sampdoria this season, scoring nine goals, and is rated as one of the brightest young talents outside the leading clubs in Italy.
Delio Rossi will be determined to keep the player at Stadio Luigi Ferraris beyond the summer, but might struggle with increased interest from the likes of Manchester City and Inter Milan in his services.