The 24-year-old penned fresh terms with the Serie A giants less than a year ago, keeping him at the club until 2021 with wages of around £80,000 a week.
According to Premium Sport, the Argentine's deal came with a release clause of €110m (£100m) for foreign clubs interested in his signature, but Inter are now worried that the clause is too low after dealings in this summer's transfer market.
Ligue 1 side Paris Saint-Germain more than doubled the previous world transfer record by spending £200m to bring in Neymar from Barcelona before committing to a £160m fee for Kylian Mbappe next summer.
With plenty of funds at their disposal, Barca then went on to sign Ousmane Dembele for a fee of £100m and £35m in add-ons, while they are believed to be plotting a bid of at least £135m for Philippe Coutinho in January.
Inter are said to be hoping to now raise Icardi's release clause to at least £190m and will also offer him an improved pay packet following recent interest in him from the likes of Chelsea, Manchester United and Arsenal.
Icardi has scored 76 times in 128 Serie A appearances for Inter to date.