The Argentina international has spent this season on-loan at PSG and has done enough to convince the Parisians to seek a permanent deal.
Sky Italia says PSG have tabled a bid of €50m up front with a further €10m due in bonuses.
Icardi's deal does carry a permanent option to the tune of €70m - which expires on May 31. However, PSG wish to renegotiate terms.
Their new offer was tabled in the last 24 hours and is now being considered by Inter's owners, Suning.