Cavani has attracted interest from Juventus and Barcelona, who have been rid of the services of Sergio Aguero because of a heart problem.
The 34-year-old joined Man United on a free transfer in the summer of 2020, scoring 17 goals in 39 appearances but has played less frequently this term.
The former Napoli man has started just three times in the league this season, scoring twice but Rangnick is keen to retain his services until the end of the season when his contract expires.
'Edi knows that I will definitely not let him go,' said Rangnick. 'He is a highly important player for the rest of the season. For me, it's clear that Edi has to stay.
'We had quite a few conversations in the last couple of weeks. He is probably the player with whom I have spoken most.
'I told him from the very first day that he is a highly important player. He is probably the only one who can play as a striker back to goal and face to goal. We are still playing in three competitions, so we will definitely need Edi.
'His professionalism and work ethic are 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. That was also the reason why I played him from the beginning together with Cristiano (against Burnley).'
