Speaking to the media on Friday, Ralf Rangnick said: "I told Dean Henderson I would like him to stay but I can fully understand he wants to play.
"He's at an age where you should regularly play as a goalkeeper but we're in three competitions and we need the three goalkeepers we have right now.
"It's the same situation as Henderson with Donny van de Beek. I had a conversation with him two weeks ago.
"I told him I would advise him to stay until the end of the season. With the World Cup coming up in the winter, he wants to play."
Both Henderson and Van de Beek have been linked with January moves away from Manchester United after hardly featuring so far this season.
The Englishman is said to be pushing to leave Old Trafford this month but the Dutchman is expected to stay until at least the end of the 2021/22 season.