The 34-year-old extended his stay at Manchester United until 2022 earlier this year but is expected to bid farewell to Old Trafford at the end of the current campaign.
Cavani has previously been linked with a return to South America with Boca Juniors, but Real Madrid supposedly believe that the Uruguay international still has a lot to offer in European football.
Los Blancos may face stiff competition for Cavani's signature, though, as El Nacional claims that Barcelona are also keen to strike a deal for the former Paris Saint-Germain attacker.
The report claims that Cavani is "not happy" at Man United after the arrival of Cristiano Ronaldo saw him pushed down the pecking order, and Barca could look to sign the striker on loan in January.
Cavani scored 17 goals in all competitions for Ole Gunnar Solskjaer's side last term but is yet to get off the mark in four appearances this season. body check tags ::