The young attacker has stressed that he is happy with life at his current club and has ruled out a transfer elsewhere
The Spanish champions allegedly saw the Argentine forward as a potential replacement for Diego Costa, who left the club for Chelsea, but they eventually opted to sign Mario Mandzukic from Bayern Munich instead.
Icardi has stressed, however, that a move to the Vicente Calderon side was never an option for him anyway.
"Atletico? Why would I ever leave Inter?" the 21-year-old told Corriere dello Sport.
"I am a key player here and I want to do well wearing the Inter jersey. I had my phone switched off during my holiday and didn't read any papers. I never even considered leaving Inter.
"A contract renewal? That's something my agent concerns himself with. I didn't speak to any of the Inter directors. I am focusing on my performances on the pitch and my personal life.
"If my agent gets in touch and tells me to come and sign a new deal, then I'll think about that."
Icardi's current deal with Inter runs until 2018.