The pair have been linked with moves in the January transfer window after finding opportunities limited this season, but Rangnick said he is keen to keep his squad together ahead of a busy second half of the season.
"I told [Henderson] I would like him to stay because he is a fantastic goalkeeper, in training yesterday he had a couple of fantastic saves," Rangnick told a news conference on Friday.
"I can fully understand he wants to play. He's at an age where you should regularly play but we are in three competitions and we need three goalkeepers right now. I can understand his desire to get regular game-time elsewhere in the Premier League."
Henderson has made just two first team appearances this season, while Van de Beek has not started a league game since May.
"It's the same situation as it is with Dean," Rangnick added.
"I'm glad to have him in the squad. He came on against Villa [on Monday] and did well and he is always performing at a high level in training.
"I had a conversation with him after training two weeks ago and advised him to stay. With the World Cup coming up in the winter, he wants to play.
"Louis van Gaal told him to be a regular starter he has to play for his team, but on the other hand, we have a lot of competition in our squad in those positions."
Rangnick is preparing his team to face Aston Villa on Saturday, just five days after beating Steven Gerrard's side in the FA Cup on Monday.
"I think they will be available," Rangnick said.
"They only trained yesterday for the first time. Cristiano yesterday, Harry the day before yesterday. We have to wait for the final training session but they should be available."