The German has signed a deal to become the club's interim manager until next May, when the Red Devils are then expected to appoint a long-term replacement for Ole Gunnar Solskjaer.
However, Rangnick, speaking during Friday morning's press conference, has said that he could recommend to the English giants that he stays on in the managerial role beyond the length of his current deal.
"The people with whom I've spoken with, they have been very clear that it is a six-and-a-half month role. We have never spoken about what will happen in the summer," Rangnick told reporters.
"If they will speak about me with that, we will see. If they ask me about my opinion, I might make the same recommendation that I did at RB Leipzig twice, that it might be better to work with me for one year."
Rangnick was in the stands for Man United's 3-2 win over Arsenal in the league on Thursday but will be in the dugout for Sunday's clash with Crystal Palace.