However, the 34-year-old’s time in England has also been beset by injury problems and a controversial ban last season for using what the English Football Association deemed racist language in a social media post.
Cavani, whose contract expires at the end of the season, has been linked with a move to Barcelona, but Rangnick highlighted his importance despite having a wealth of attacking options to choose from.
“We spoke about Edi and he knows that I will definitely not let him go,” said Rangnick ahead of United’s Premier League clash with Wolves on Monday.
“For me, he is a highly important player for the rest of the season, still playing in three competitions, so we will definitely need Edi.
“I would rather have another Edi on top of that but for me it’s clear that Edi has to stay.”
Cavani started for the first time under Rangnick in Thursday’s 3-1 win over Burnley.
And the German believes he and Cristiano Ronaldo can form a potent partnership despite having a combined age of 70.
“He is probably the only one who can play as a striker back to goal and face to goal,” added Rangnick on Cavani.
“His professionalism, his work ethic is just amazing and I told him that I desperately want him to stay until the end of the season. He knows that.
“He also knows how highly I rate him and how highly I respect him, and that was also the reason why I played him (against Burnley) from the beginning together with Cristiano.”
Anthony Martial is one of United’s forward options who looks set to leave in January with Sevilla reportedly close to agreeing a loan deal for the French international.
Dean Henderson, Jesse Lingard, Juan Mata and Donny van de Beek could also move on in search of more first-team action.
But having just got over a coronavirus outbreak among the United squad, Rangnick said he may have to retain a larger pool of players for the second half of the season due to Covid considerations.
“Our squad is maybe a little bit too big with regards to numbers,” said Rangnick.
“But we still have Covid, we have three competitions, as I said, and I think we could do with a bigger squad than maybe in times without Covid.”