Costa has netted just five goals in 21 matches for Los Rojiblancos this season and it has been reported the club are open to a sale this summer.
The Spain international refused to train with his Atletico Madrid teammates on Thursday last week after the club opened misconduct proceedings into his red card at Barcelona.
The striker was shown a straight red card during the loss at Barcelona earlier this month by referee Gil Manzano, who stated in his post-match report that Costa insulted his mother.
The report now claims that video footage has proved that is not the case and Atleti will now seek to internally punish the player.
Costa has been linked with a summer move to a club from the Chinese Super League.
Cavani’s contract in the French capital expires next summer and he has scored 192 goals across six seasons at the French giants.