The Argentine striker, 25, is under contract until 2021 but the club has been negotiating a new deal with his wife Wanda Nara, who acts as his agent.
Inter coach Luciano Spalletti called for a resolution after Saturday’s win over Parma with goalkeeper Samir Handanovic named the new skipper.
The club tweeted: “Samir Handanovic is the new Inter captain.”
The Slovenia international, 34, joined Inter from Udinese in 2012 while Icardi arrived from Sampdoria in 2013, taking over as captain from Andrea Ranocchia in 2015.
Icardi, who has eight caps for Argentina, scored 122 goals in 208 appearances for Inter, who are currently third in Serie A, 20 points behind leaders Juventus.