The 28-year-old has only managed 13 appearances this season, with his last Premier League outing ending with a red card against Liverpool. It had been a strong start to his campaign, with four assists in the opening day rout of Leeds.
“As far as I know, I was told a week ago, it would be a minimum of at least another four or five weeks before he is fit for training again,” Rangnick told the club website.
“I saw him this morning before the training session, he was in the locker room, and I hope he will be back as soon as possible.
“Right now, he’s not been part of the training group and, even if he was back whenever, two, three or four weeks, it will take some time.
“It’s one thing to be training fit but, on the other hand, he needs to be fit for the match and competition in either the Premier League or the Champions League and this will still take some time.”
United face Aston Villa in the FA Cup on Monday night and Rangnick will make limited changes to his side with Victor Lindelof back available after a spell out with Covid-19.
He added: “We will definitely not play with eight or nine different players. Or even 10, as we did against Young Boys in the Champions League.
“We will try to play with the best possible team, with a strong team. There might be a few changes but I haven’t taken the final decisions yet myself. We will definitely try to play this game as if it was a normal Premier League or Champions League game.”