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The Uruguayan forward is out of contract at the end of the season and has been linked with a January move to Barcelona.
A combination of injuries and the summer arrivals of Cristiano Ronaldo and Jadon Sancho mean Cavani has not always been a regular for United this season, but he scored off the bench against Newcastle last month and was rewarded with a start in the 3-1 win over Burnley last time out.
“We had quite a few conversations in the last couple of weeks - probably the player with whom I have spoken most,” Rangnick said ahead of Monday’s clash with Wolves.
“I told him from the very first day that, for me, 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.
“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.”