Inter would prioritize Roberto De Zerbi over other options for the bench if they sacked Simone Inzaghi, which is increasingly likely.

De Zerbi Tops Inter List of Candidates for the Bench

Simone Inzaghi is highly likely to get sacked if he doesn’t regain the trust of the management through strong performances in the remainder of the season. If it indeed happened, Inter would prioritize Roberto De Zerbi over other options. He has done well in the Premier League with Brighton.
Simone Inzaghi needs to finish strong to stay at the helm, but Inter have already started mulling their options in case they indeed axed him.

Inter Focusing on Three Names in Early Coaching Search

Simone Inzaghi needs to finish strong to stay at the helm, but Inter have already started mulling their options in case they axed him. Reuniting with Antonio Conte is a strong possibility, although there isn't unanimous approval about that within the club. There haven't been direct contacts with the ex-Italy boss.
Conte Inter Juventus

Spurs Draw Five-Man Shortlist to Replace Italy-Bound Conte

Antonio Conte and Tottenham Hotspur parted ways after 16 months by mutual consent after the Italian tactician blasted the club and its players in a remarkable interview. It is unclear whom Daniel Levy and Fabio Paratici will hire in North London to succeed the ex-Chelsea and Inter manager.
Despite the UEFA Champions League final encounter against Manchester City looming on the horizon, Inzaghi is confident of seeing his team focused.

Inter and Atalanta Bosses Rumored to Be on the Hot Seat

The upcoming summer could be particularly busy in terms of coaching changes. Several Serie A teams, including some high-profile ones, are considering moving on from their current gaffers, especially if they don’t fare convincingly in the remaining portion of the season. Inter, Atalanta, Fiorentina, Torino, and Sassuolo might hire new managers.
De Zerbi seems to have the magic key to unlock a player’s potential and has no issue in turning to youth, as he's showing at Brighton

Roberto De Zerbi: Bringing Calcio to the South Coast at Brighton

His predecessor, current Chelsea boss Graham Potter, had a turbulent relationship with those in the stands and would undermine their importance to the media. By De Zerbi having The Amex behind him, it meant he had time for his footballing philosophy to come to fruition, an unbeaten January shows it already has.