The striker will be free in June when his contract with the French champions expires, but Diego Simeone believes he add significant firepower to his team.
Although Atletico have the third best defensive record in La Liga, they have the worst goal tally of the Spanish division's top seven teams, scoring just 22 goals in 20 matches.
The Rojiblancos, currently third in La Liga and eight points behind leaders Barcelona, are eager to invest in an experienced striker in the January transfer window.
And they see the 32-year-old, who has proved prolific in Italy and France, as the solution to their problem.
PSG, however, are determined to hold on to the ex-Napoli and Palermo star, as sporting director Leonardo continues to block Atletico's advances for him.
Furthermore, coach Thomas Tuchel says he would rather hold on to the forward, believing he can still play a key role in their hunt for Champions League and Ligue 1 titles this term.
Even PSG president Nasser Al-Khelaifi is convinced that Cavani's presence could be pivotal in their European campaign, despite his diminished role in the squad this season.
Cavani has made just 14 appearances in all competitions, limited mainly as a result of the injuries he has suffered this term, but he has still managed to score five goals in that time.
While the key figures at PSG have no interest in letting him go, Atletico do not want to give up on the Uruguay international.
As well as their latest €10m offer to PSG, the Madrid outfit are offering Cavani a €12m (£10m/$13m) per season salary to lure him to the Spanish capital.
Their attempts may have been dismissed by the French giants, but Atletico will continue their efforts until the transfer window closes at the end of the month.
Having joined PSG from Napoli seven years ago, Cavani has made 293 appearances for the French side, scoring 198 goals as he helped fire them to five Ligue 1 titles and plenty more domestic trophies.