Stamford Bridge boss Jose Mourinho requires another striker, with Fernando Torres and Demba Ba their only established Premier League centre-forwards, and Cavani has emerged as the club's principal target following the transfer of the coveted Colombian Radamel Falcao from Atletico Madrid to Monaco.
Wanted man: Edinson Cavani is a target for Chelsea and Real Madrid
Former Chelsea interim manager Rafa Benitez will coach Napoli next season and club president Aurelio De Laurentiis insists that Cavani will not be sold unless the Olympian €60m buy-out clause is met for a forward who was Serie A's top scorer last season with 29 goals.
Manchester City, who were previously monitoring Cavani, have cooled their interest in the player, with new Chilean manager Manuel Pellegrini understood to feel he would be unsuitable for the style in which he wants to play.
It means that Real Madrid and Chelsea remain the most interested parties, with the west London club hoping that their early moves in the market will encourage the player to join them rather than wait for a possible offer from the Bernabeu.
Real Madrid president Florentino Perez and their new coach, the former Chelsea manager Carlo Ancelotti, want to move for Liverpool's Luis Suarez - Cavani's international team-mate.
But Real are likely to opt for Cavani if the task of prising Suarez from Anfield proves to be too expensive.
Chelsea clearly need another centre-forward to bolster the current trio of Torres, Ba and Romelu Lukaku, 20, who spent last season on loan at West Bromwich.
Ancelotti target: Luis Suarez could move to Real Madrid
That idea has since been dropped and Belgian Courtois, 21, will remain on loan at Atletico Madrid for a third consecutive season.
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