Cavani, 33, is available for free after his contract with Paris Saint-Germain expired in June and he has been offered to a number of Europe's biggest clubs.
Sources have told ESPN the Uruguay international has already held talks with Juventus and he would be keen on a return to Italy, with his children still residing in Naples.
Juve are looking for a replacement for Gonzalo Higuain, who has joined Inter Miami, and sounded out Cavani before they ruled out a move for Barcelona's Luis Suarez last week. Atletico Madrid's Alvaro Morata is also an option, sources have confirmed.
Madrid, meanwhile, were not initially looking to strengthen their squad due to the financial implications of the coronavirus pandemic but several sources have told ESPN they are now considering changing that stance.
However, to sign Cavani, they would first need to shift some of the excess forwards they have in the squad before the transfer window closes.
Zinedine Zidane's side's problems in front of goal were once again in evidence on Sunday as they kicked off the La Liga season with a goalless draw against Real Sociedad.
Jovic and Mayoral were both unused substitutes against Sociedad, with Zidane not turning to either despite Madrid's need for a goal, while Mariano missed out with tonsillitis.
ESPN reported in July that there was a clamour inside the club for a new attacker to arrive to take the weight off Benzema.
Despite that, Madrid managed to beat Barcelona to the La Liga title thanks to 10 wins in their final 11 games but there's an acknowledgment they will need to improve to compete in Europe this season.