The 24-year-old has scored nine Serie A goals in just eight appearances this season, and netted a famous hat-trick in Inter's 3-2 win over AC Milan at San Siro last weekend.
Icardi is understood to currently have a release clause of £98.2m, which will expire on July 28. However, according to Calciomercato, Inter want to increase the buyout figure to £133.9m in order to protect the value of the in-form striker.
Icardi spent time with Barcelona during his youth career before turning professional at Sampdoria in 2012.
The four-time Argentina international has scored 87 goals in 154 appearances for Inter following a 2013 move to the Milan giants.