Maguire was installed as skipper by former boss Ole Gunnar Solskjaer shortly after his £80 million move from Leicester in 2019.
There have been suggestions that the speed at which Maguire was handed the armband combined with his run of poor form this season has caused tensions within the dressing room and Rangnick insists the best way to solve the issue is to let the players elect their leader.
"I strongly believe the captain should be elected by the team because he's called the team manager and we always did that, we always had a board of four or five players -- we called it the 'Spielerrat' [players' council] -- elected by the players," Rangnick said.
"The player with the highest amount of votes was the team captain at the end. That was how I did it. I know a lot of head coaches don't do it that way.
"That's what I would do if I was still the manager next season but in the end I'm not. This is something that Erik [ten Hag] will have to decide."
Rangnick is set to take up a two-year consultancy role at Old Trafford from the end of the season and says he will be on hand to advise Ten Hag if and when it's required.
The pair are yet to speak following the Dutchman's appointment with Ajax still in the hunt for the Eredivisie title.
"I'm looking forward to working in that advisory role and obviously helping Erik as much as he wants it himself," Rangnick said.
"So far we haven't been able to speak with each other and we have had no contact. He has his focus on Ajax, I have my focus on Manchester United here.
"Obviously I'm more than willing and prepared to help both Erik and whomever in the club in order to change everything for the better."
Work has already started on identifying targets for key positions but Rangnick said Ten Hag is likely to get the final say on any new arrivals.
"I can only tell you what I'm used to in Europe or in Germany, and as you know in almost all clubs there is a sporting director who together with the manager or with the head coach and the scouting department is responsible for which players will be coming," Rangnick added.
"For example in my last two clubs, we never signed a player without the approval of the manager.
"I'm pretty sure this will also be the case here with Erik. I'm also positive that Erik will make some suggestions and then together with the board, together with the scouting department and possibly myself, we will then decide on the right players.
"I have never and we have never signed a player at Red Bull -- neither at Salzburg or at Leipzig -- against the proposal or the wish of the head coach."