The Uruguayan has scored 19 goals in 49 games for the Red Devils since joining the team in October 2020 on a free transfer.
However, the 34-year-old has also been plagued by injury problems and a controversial penalty last season for using racist language in a social media post, according to the English Football Association.
Cavani, whose contract expires at the end of the season, has been linked to a transfer to Barcelona, but Rangnick stressed its importance despite having several forwards to choose from.
“We talk about Edi and he knows I will not let him go,” Rangnick said at a press conference before the game against Wolverhampton in the Premier League on Monday.
“He is probably the only one who can play as a forward on defense and up front,” added the German coach, praising his professionalism.
Rangnick also stressed that he could form a complementary couple with star Cristiano Ronaldo. The two played together in a 3-1 win over Burnley on Matchday 20.
“He knows how much I value and respect him, and that is also the reason why I made him play (against Burnley) from the beginning with Cristiano,” said the coach.
Among those who could leave in January is forward Anthony Martial, as Sevilla is close to agreeing a loan for the French international.
Dean Henderson, Jesse Lingard, Juan Mata and Donny van de Beek could also go in search of high-level teams.
However, after a coronavirus outbreak among team members, Rangnick said he may have to retain more players for the second half of the season.
“Our squad is maybe too big in numbers,” Rangnick said. “But there is still covid, we have three competitions, as I said, and I think we could use a larger squad than in times without covid,” he added.