Ralf Rangnick will lead the Red Devils for the remainder of the 2021-22 campaign before taking on a two-year consultancy role at the club.
However, according to Corriere dello Sport, the 20-time English champions have made contact with Inzaghi to discuss his availability at the end of the season.
Inzaghi was in charge of Lazio between 2016 and 2021 before becoming Antonio Conte's replacement at Inter ahead of the 2021-22 campaign.
The 45-year-old has guided the Italian champions to 19 wins, five draws and three defeats from their 27 matches in all competitions this season, and the Black and Blues currently sit top of Serie A, while they beat Juventus to win the Italian Super Cup on Wednesday. body check tags ::