Perisic's current deal runs to June and has impressed for new coach Simone Inzaghi.
But La Gazzetta dello Sport says the 32-year-old Croatia international has been warned that his current €5m salary is out of their budget.
Inter are suggesting he accept a drop to €3m-a-season if he wants to remain at Inter.
Perisic has scored once in eight games for the Nerazzurri.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!