The 25-year-old arrived at the London Stadium during the January transfer window and made 14 appearances to help the Hammers avoid relegation from the Premier League.
While the east London club are keen on another loan deal, Inter want to sell the player permanently and want a fee of £25 million in exchange for his sale.
At the end of last season, Mario said: "It has been an amazing experience for me.
"I want to say thank you to West Ham for everything they have done for me as well as my teammates, and my coaches. I am really happy with the last six months and we will see what happens."