After spending a number of years in France, 31-year-old Cavani is eager to move away from the French capital this summer following a breakdown in his relationship with record-breaking summer signing Neymar.
The striker, who has scored 28 league goals this season, had also been linked with Chelsea as a potential replacement for Alvaro Morata. However, it seems that Uruguay teammates Diego Godin and Jose Gimenez have convinced Cavani to join them at the Wanda Metropolitano next season instead.
27-year-old Griezmann, meanwhile, is reportedly close to completing a move to Barcelona, in a transfer which has been on the cards for months. The Catalan club are long-term admirers of the French forward, with club president Josep Maria Bartomeu recently revealing that he met with Griezmann's agent earlier this season.
Atletico chief executive Miguel Angel Gil Marin responded by saying that the club were "fed up" with Barcelona's pursuit of Griezmann.
The report by Mundo Deportivo goes on to suggest that Atletico had previously been interested in replacing Griezmann with Juventus star Paulo Dybala, but were put off by the high asking price which would have eclipsed Griezmann's £89m release clause.
Cavani has scored an impressive 170 goals in 245 appearances for PSG since arriving from Napoli in 2013, helping the club to win four Ligue 1 titles.
Atletico manager Diego Simeone is said to be confident that acquiring the Uruguayan forward will be the key to challenging Barcelona's firm grip on La Liga next season. The club currently lie in second place, a considerable 15 points behind the unbeaten Barça with local rivals Real Madrid sitting just three points behind them in third.