Several reports in the English tabloids have focused on tension in the Manchester United dressing room over the issue.
Maguire has come out on social media to deny the rumors and now his manager has doubled down on his pronouncements.
"Well, to start with, I must say this is absolutely nonsense," Rangnick told reporters ahead of Sunday's clash with Leeds United.
"I have never spoken with any player about a possible change of captaincy, Harry was fully aware of that, so was Cristiano and the other players. This has never been an issue for me.
"It's me who decides who's the captain and therefore there is no reason for me to speak about that with another person. Harry is our captain and he will stay our captain until the end of the season and there is nothing else to add on to that."
"Well I'm not frustrated at all because I know it's not true," he continued. "I told you about Harry being the captain, it's not an issue at all, it's never been an issue for us or myself as manager.
"All the other things, to be honest, I don't listen to that noise that much because my full focus is on preparing the team for the next training, for the next game.
"Obviously, I have heard about what was written. I can only tell you from my personal experience in the last 12 weeks, yes, there were players unhappy until the closure of the transfer window because, as I always said, the squad was too big, we had too many players who just realised they wouldn't get game time and this has improved, for sure.
"From what I can tell, the atmosphere in the locker room is better than it used to be a couple of weeks ago for all those reasons I just spoke about.
"As you quite rightly said, for us it's about performing well, showing togetherness on the pitch, getting the best out of our performance and winning games, that's our job. Those are the things we can influence, all the other things we can't."
