The Italian media report he has a big offer from Saudi Arabia so if he actually leaves Inter he's probably going there. Also because I don't think he can go anywhere in Italy right now: Milan and Roma just hired new managers, Napoli confirmed Conte, for sure he won't go back to Lazio. The only team left would be Juventus but it's almost impossibile that he leaves Inter (still having a contract) to join Juventus, no way.
I believe that Inzaghi will stay with Inter Milan and fight for a third Champions League final match and aim at winning this title with them. He will not accept that he won't be able to win Champions League title and moving to any club even big one in Europe now is risky for him. He has built up a competitve team in Inter Milan and has gotten good foundation to win this trophy.Inzaghi will sit down, talk with Inter Milan board members for improvement of the squad and return to a next season with a stronger team for winning Scudetto and Champions League.
I understand him anyway, it's a lot of money and his cycle with Inter was at the end because losing 2 Champions League finals in 3 years takes a toll on you, it happened the same at my team back in 2015 and 2017. Inter at this point need to change a good amount of players that are just too old, there are a lot of 30+ years old, and let's not forget that at the end Simone Inzaghi only won one Serie A in four years so he did some very good things but the final results were so and so.