Inter are moving on with keeping Inzaghi in the manager position. I think they are doing the right thing as well. Because I call their last season performance successful. They won two titles like Coppa Italia and Italian Super Cup first of all. After that they qualified for the Champions League finale and made quite big difficulties for Manchester City there as well. Maybe they weren't in a title race in the Serie A. But there was a reason for that as well. They couldn't start the season well and it was late when they started to do better.
They had defensive issues at the first times of that season. They should make sure now that they don't have the same experience this season.
I've never seen any news about Inzaghi, I didn't think he would leave the team. In the past years, there were news that he would move to other teams, but I did not come across such a thing for this year.
Right now Inter has bigger transfer news. There are rumors that Lautaro Martinez will leave the club and go to Saudi Arabia. In addition, goalkeeper Andre Onana also moved to Manchester United. It seems that there will continue to be names leaving the team

It is too soon and also too young for Lautaro Martínez to play in the Saudi Professional League but indeed, if Lautaro Martínez accepts the offer to play in the Saudi Professional League then Lautaro Martínez will earn a very large salary. Maybe, there are also those who say it is 10 times more than his salary at Inter and yes, if Lautaro Martínez is financially focused so this offer can be accepted. But even so, I personally am not entirely sure that Lautaro Martínez will accept the offer at this moment but about Onana. It looks like maybe Onana's move will really happen at this moment because yes, Manchester United also did not extend De Gea's contract which made Manchester United need Onana to be included in Manchester United's main squad next season.