Why not? He's done great at Lazio. His work there is comparable to Poch's work here. And Simone won titles as well doing it so he has that going for him.
Lazio before Inzaghi: 4th, 7th, 9th, 3rd, 8th (Inzaghi took over as caretaker in April)
Lazio with Inzaghi: 5th, 5th, 8th, 4th, currently 6th
Spurs before Poch: 5th, 4th, 5th, 6th
Spurs with Poch: 5th, 3rd, 2nd, 3rd, 4th
Inzaghi has won a Coppa Italia and seen Lazio into the CL group stages, all on a limited budget. But he hasn't taken the club up a level the way Poch did.
Anyway, this smells like contract negotiations with Lazio, the club Inzaghi has been at in one role or another since 1999.