As a proven goal-getter at the very highest level, the 25-year-old frontman has no shortage of suitors.
Sides across Europe would welcome the opportunity to bring him onto their books and are aware that his current deal at San Siro includes a €110 million (£96m/$126m) release clause which can be activated in the first two weeks of July.
Inter are eager to remove that condition from Icardi’s terms, while also extending his stay in Milan.
He is already tied to the club until 2021 but sporting director Piero Ausilio admits talks are being planned, telling Sky Sport Italia: "From our side, there is the desire to improve his terms and renew his contract, while on his side there is collaboration.
"Since he has three years left to run on his contract, it's possible that we do it in a few days or in a few months, but it's not a problem."
Icardi’s agent Wanda Nara, who is also his wife, recently revealed that no contract discussions have been held as yet.
Inter appear keen to get that process started, with Ausilio pleased with the progress being made by the club under the guidance of Luciano Spalletti.
He added: "The team has character. To achieve important things also takes quality, and Inter have shown themselves to have that in recent games.
“We are trying to improve. Inter is aware of the work it has done so far. We are coming off a positive season in which the goal was to return to the Champions League, and we succeeded.
“We will now play our cards in the Champions League and in Serie A. The work of the last few weeks is the basis for building an even stronger Inter.
“We have included several new players who arrived after the World Cup and it was inevitable that there would be some initial difficulties.
“We are aware of the need to be strong and we want to prove that in the derby.”
Inter return to domestic action after the international break with a clash against old adversaries AC Milan on October 21.