Marca says the brother and agent of the striker is in Madrid, drawing up the details of the contract that may, or may not, eventually be signed.
Despite the wishes of Atletico and Cavani for the move to go ahead, its completion still hinges on PSG.
Atletico have offered ten million euros plus variables which was turned down, and would be willing to offer 15 million euros.
The Ligue 1 champions started the January transfer window refusing to negotiate any move for Cavani but then altered their stance, placing a 30 million euro price tag on the soon-to-be 33-year-old.
Yet Los Rojiblancos are refusing to pay more than 20 million euros for a player who is available for free in June.