Giuseppe Marotta, Inter's chief executive, recently told the striker he was no longer wanted and a divorce appears to be nearing fruition.
Icardi left the Nerazzurri's training camp in Switzerland on Saturday and will be excluded from upcoming friendlies against Manchester United, Juventus and Paris Saint-Germain.
.@MauroIcardi will today return to Milan from our training camp in Lugano. The club and the striker have come to this decision by mutual agreement. Icardi will continue his pre-season training over the next few days and will take no part in our Summer Tour in Asia.#FCIM— Inter (@Inter_en) July 13, 2019
Inter confirmed the development in a statement published to social media.
It read: "Mauro Icardi will today return to Milan from our training camp in Lugano.
"The club and the striker have come to this decision by mutual agreement.
"Icardi will continue his pre-season training over the next few days and will take no part in our summer tour in Asia."
Whether Inter can find an appropriate suitor for their controversial former captain remains unclear.
Juventus have been linked and Napoli president Aurelio De Laurentiis, who admitted to being interested, has claimed Icardi is set on a switch to the Serie A champions.
The 26-year-old has spent six seasons at Inter.
Antonio Conte's men meet local Swiss side Lugano on Sunday before jetting off to face Premier League outfit United in Singapore.