Fortunately EPL clubs consider De Zerbi a safer bet than Inzaghi
Inzaghi would be crazy to go to Chelsea or Man Utd. Chelsea keep blaming coaches while the real problem is their recruiting policy. Inzaghi would walk into a giant mess if he went there. As for Man United, there's too much uncertainty there. Club needs big reinforcements and no one knows what Ratcliffe really plans to do. Their desired sporting director was put on gardening leave by Newcastle and it's uncertain when this is gonna be cleared out. Too big of a risk for a top coach to go to Man Utd right now.
Liverpool would be a good option for him but they seem more focused on Alonso, Nagelsmann, Amorim and De Zerbi. Barcelona would be a concrete option as well but i don't think he suits their style. I can't see Barcelona playing with 3-5-2. I could see Tuchel or Flick ending up there.
I doubt he will be considered by Bayern. It's unlikely they will take a risk with someone who doesn't even speak the language. After the names i had listed in another post, there's even a rumour about a Nagelsmann return now that Kahn and Brazzo are gone. Real are sticking with Ancelotti and they will eventually turn to Alonso so i don't think he's an option for them.
In the end, the most likely scenario is Inzaghi will sign an extension with a salary increase at the end of the season.