Do you know if the management highly regards him and Inzaghi doesn’t see the potential?
Management serves the coach's needs in the way they see fit or are able to operate given the restrictions, that's all that can be said.
If Inzaghi rates a player, management won't seek to send hin away.
If he doesn't rate a player and wants a replacement, if it's feasible they'll look to accommodate that.
For example last season Gagliardini couldn't be moved. Nor the year before. He refused all destinations presented whether they were Serie A, PL or some fringe league's team.
If Asllani decides that he'll be better off somewhere else, be it Sassuolo or another team, and we can pull a deal off without enforcing the Zhang buzzer, an incoming (loan/free) transfer will take place.
Don't think there's any players left to sell now, so transfer budget won't be affected.
I can tell you for a fact that Inzaghi would appreciate 2 new midfielders and 1 new striker. But this has to come at zero added cost.
Remember that in terms of quantity, the bare minimum was to add another midfielder (eg Samardzic), and we don't have someone else yet.