The injured attacker is desperate to leave Villarreal in order to return to his native Italy this summer, and has caught the attention of the Serie A giants
The Partenopei are in the market for attacking reinforcements following the departure of Ezequiel Lavezzi to Paris Saint-Germain earlier this summer, and they see the 25-year-old as a valuable addition to their squad.
The forward is available on the cheap, given Villarreal's relegation to the Segunda Division last season, and an offer in the region of 7-8 million euros could be enough to lure him away from his current club.
The Partenopei are hopeful of getting Rossi even cheaper, though, as they are preparing an offer of 5 million euros plus bonuses.
Nevertheless, Napoli faces stiff competition in the race for Rossi's signature as Inter is also closely monitoring the attacker's situation.
Inter has made Brazil international Lucas Moura its primary transfer target this summer, but it considers the Italy international to be a capable alternative in case the club fails to lure the Sao Paulo winger to the Giuseppe Meazza.
Rossi is currently sidelined due to a knee injury which also kept him out of Euro 2012, but is nonetheless hopeful of securing a transfer to a top club in Italy, with his agent working hard to broker a deal.