Rangnick has identified the Bayern Munich manager as one of the potential targets to lead the Red Devils in future.
It has also been reported that Ragnick would have his say on who should be the next manager to lead the Red Devils from next season onwards.
The young German gaffer took the reins at Allianz Arena last summer after agreeing to a contract until 2026.
Rangnick had previously worked with Naglesmann at RB Leipzig and both played a key part in the German outfit becoming one of the recognisable forces in Europe.
Nagelsmann has often cited Rangick as his major influence, and so have been the fellow German managers Thomas Tuchel and Jurgen Klopp.
Nagelsmann has recently offered his views on the prospective arrival of Rangnick to Old Trafford, stating that the veteran manager would do a good job in the Premier League.
However, it remains to be seen whether the former Leipzig boss would part ways with Bavarians just after a season.
Pochettino is apparently interested in taking over at Old Trafford, with the reports stating he is unhappy at the French capital.
Ten Hag has recently shrugged off the speculations, insisting that he is focused on his current role at the Dutch club.
Michael Carrick has been overseeing the Red Devils on a makeshift basis following the departure of Ole Gunnar Solskjaer.
In his first game in the charge, the former midfielder led United to a comprehensive win against Villarreal in the Champions League.