Rangnick took over at Old Trafford on an interim basis in late November, replacing Ole Gunnar Solskjaer at the helm.
The German is tasked with leading Manchester United until the end of this season and is then to take a consultancy role at the club for at least a further two years.
Manchester United’s hierarchy are on the lookout for managers to fill the Old Trafford hot seat next summer on a permanent basis.
And according to Italian daily Corriere dello Sport, the Reds Devils, along with La Liga champions Atletico Madrid, have registered an interest in Inter coach Inzaghi.
The 45-year-old took over at Inter in the summer, succeeding Antonio Conte and has had positive start to his spell at the San Siro.
Inter entered the season following a tough summer break which saw the departures of Conte, the coach that took them back to the Serie A title last season, and key player Romelu Lukaku.
However, Inzaghi has not let the standards drop at Inter, with the side on course to clinch consecutive league titles, while also making it into the knockout stages of the Champions League.
It remains to be seen whether the Inter coach will become a serious target for the managerial role at Old Trafford in the coming months.