The 25-year-old, who spent last season on loan at Everton, is available on a free transfer following his release from Real Madrid.
It has been reported that Inter Milan are also keen on the winger.
Antonio Salerno, Drenthe's agent, said that his client would welcome a move to Serie A.
"Royston has told me on several occasions that, after showing his worth in Spain and England, he would like to play in another top league like Serie A," Salerno told Tuttomercatoweb.
"We have made contact with several top-flight clubs and we are awaiting responses. Napoli, Palermo and Lazio are just some of the clubs we have spoken to.
"Drenthe's technical qualities are well known. He plays on the left flank and is very strong in attack but can also be used in defence as a full-back. He's a player of a very good level and has a strong desire to test himself again."