Speculation over the Argentine forward's future has been rife, with Goal having reported that new manager Antonio Conte is keen to see him depart in the summer transfer window.
That saw the 26-year-old linked with a switch to Juventus, although the Serie A champions are not interested in a potential swap deal that would involve forward Paulo Dybala.
Juve are also conscious that they have a large squad that possesses a number of attacking players that can play in Icardi's position, including the likes of Dybala, Cristiano Ronaldo, Moise Kean, Mario Mandzukic and Gonzalo Higuain.
Sources have told Goal that for Maurizio Sarri's side to potentially make a move for Icardi, Mandzukic, who only signed a new two-year contract with the club back in April, and Higuain would likely both need to be moved on.
Despite Juve not currently being interested, Icardi's return to Milan would appear to provide the opportunity to negotiate a potential exit from San Siro.
An Inter statement read: "Icardi will return to Milan from the Lugano training camp today. The club and the Argentine striker have made this decision by mutual agreement.
"Icardi will continue on his path of athletic reconditioning in the coming days but will not take part in the summer tour in Asia."
Napoli are another side who have been linked with a move for the striker, although the club's president Aurelio De Laurentiis labelled reports of a meeting with his agent and wife Wanda Nara "colossal, enormous stupidity."
La Liga giants Real Madrid have long been suggested as a potentially interested party, although Icardi's preference is to remain in Italy and it would seem unlikely Zinedine Zidane's side would make a move given their huge spending already this summer.
Despite Icardi's reluctance to move abroad, he does still have a €110 million (£98m/$125m) release clause that only applies to clubs from outside of Serie A.
The former Sampdoria striker, who joined Inter in 2013, has not been far from controversy during his time at San Siro and he was stripped of the captaincy earlier in 2019.
Indeed, the club's current skipper Samir Handanovic has called for players to respect their "duties towards the club", while chief executive Giuseppe Marotta has already confirmed that Icardi is not in Inter's plans for the 2019-20 season.
Icardi has scored an impressive 124 goals in 219 games for Inter, with 111 of them coming in the league.