Rangnick is in the final weeks of his spell as United’s interim manager before he passes the reins to Ajax boss Ten Hag in time for next season.
The German has written off sixth-placed United’s hopes of qualifying for next season’s Champions League via a top-four finish in the Premier League.
United go into Thursday’s game against Chelsea looking certain to have to settle for a Europa League or Europa Conference League berth, and Rangnick fears the demands of those tournaments could hinder Ten Hag in his first campaign.
“It could be an advantage (missing out on European football) but that does not mean that we will give away any of the remaining four games,” Rangnick told reporters on Wednesday.
“For us it’s clear and this is our obligation, this is our job, my job, the job of the players that we try to get the best possible results and then we will see at the end of the season in which position we will finish.
“But now to speak about ‘Would it be an advantage or not?’ doesn’t make sense because if I did that then this would be interpreted again.”
Rangnick starts a two-year consultancy role with United at the end of the season, but has admitted the make-up of the position remains unclear.
The 63-year-old expects to find out more in the coming weeks and he wants to help Ten Hag in any way he can.
“Yes I will be (here next season),” he said. “I’m looking forward to working in that advisory role and obviously help Erik as much as he wants it himself.
“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.
“But 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.”
Rangnick also thinks Ten Hag should put United defender Harry Maguire’s role as club captain to a vote of the team after his wretched season.
“I strongly believe that the captain should be elected by the team because he’s called the team manager and we always did that,” he said.
“That’s what I would do if I was still the manager next season but in the end I’m not, so this is something that Erik will have to decide.”