The defending La Liga champions are reportedly set to use France international Karim Benzema as part of a lucrative package to bring Cavani to the Bernabeu.
Chelsea and Manchester City have both been long-term admirers of the Uruguyan international, but reports in Italy claim Real Madrid are prepared to kick-start a bidding war between the continent's richest clubs to land the forward.
According to Italian newspaper TuttoSport, Madrid will offer £25m plus Benzema, and the mega offer could be enough to persuade Napoli to finally cash in on their star asset.
If the reports are correct, talkSPORT claims Paris St-Germain, Chelsea, Manchester City, and a host of Russian clubs would be interested in submitting their own offers for the striker - sparking a race to the highest bid.
The 26-year-old is under contract at Napoli until 2017, and the Serie 'A' club are going well in their domestic league, currently occupying second spot behind Juventus.
Cavani is Serie 'A' top scorer, with 18 goals from 22 league appearances so far this season, and the report claims his good form is likely to ratchet up interest from Spain and England for his signature come the end of the season.
Chelsea signed Demba Ba in January, but sold Danny Sturridge to Liverpool in a deal believed to be worth around £12m. And Manchester City also sold a striker of their own - offloading Mario Balotelli to AC Milan.
As a result, both Premier League clubs are expected to explore their options at the end of the season, with a view to strengthening their squad.