But Rangnick says Cavani, who is out of contract in the summer, has committed to staying until the conclusion of the season.
"I told him I wanted him to stay," Rangnick added.
"I spoke with him [on Thursday]. He came into my office and we talked for over 30 minutes about staying until the conclusion of the season.
"For his own sake, he stayed until the end of the season and gave his all, as a role model for the young players.
"If he needs to play right away, he's ready and willing.
"Even if he doesn't play, he will attempt to be the finest role model for the other players, which is excellent news for me."
On Monday, United and Rangnick host Aston Villa in the FA Cup.
Rangnick has promised to field a tough team against Steven Gerrard's Villa.
Despite losing their past two games against Chelsea and Brentford, Villa have climbed to 13th in the table since Gerrard's arrival.
The winner will face Middlesbrough in the fourth round.
"I've always loved the FA Cup," Rangnick stated.
"It's a big competition for me. We shall aim to field our strongest team possible in that game. We take the game seriously and want to move one round ahead if we beat Aston Villa.
"We know it won't be easy because they've been doing well since changing management. They won four and lost four, three to the top team. Our performance is critical to its success."
-7msport
