Cavani, 33, has been offered a one-year contract that can be extended by a further year if Atletico qualify for the Champions League.
The Rojiblancos have told Cavani that he would have to accept less than the €10m salary he earned at PSG.
Cavani believes Atletico would be a good club for him and would see him link up with Uruguay teammate Luis Suarez.
Suarez’s move from Barcelona to Atletico has not ended the club’s interest in Cavani.
The Costa Problem
But before any move can happen, Atleti will first have to sell Diego Costa.
Costa has a €10m-per-season salary and has not yet found a club willing to match that.
The market closes on October 5 in Spain and Atletico have until then to find him a new club.
According to Radio Marca, Cavani’s camp has granted power of attorney to René Ramos, brother of Sergio Ramos, to negotiate a transfer to Madrid.
Cavani has a preference to play in La Liga and would be happy to wear the shirt of either Madrid club.