The Serie A outfit have turned their attention to the Netherlands international, while they are also keen on his PSV team-mate Dries Mertens
The Netherlands international has long been linked with a move to a bigger league, with Manchester United among the teams reportedly keeping a close eye on the 23-year-old.
Nevertheless, Napoli now seem to be leading the race for Strootman, who is currently in action at the European Under-21 Championship.
"Napoli's interest is pretty serious. They have already approached us," Strootman's agent Chiel Dekker told Voetbal International.
"Kevin's focused on the Under-21 Euros for now, though."
A move to Napoli is by no means a certainty yet, however, as Strootman's preference remains a move to the Premier League.
"Kevin's never made it a secret that he has a preference for the Premier League," added Dekker.
The midfielder has a contract with PSV until the summer of 2016, but could be available for a fee in the region of €15 million [£12.7m].
Meanwhile, Napoli are closing in on Dries Mertens as well, as they see the PSV winger as a valuable addition to their attack.
Sporting director Riccardo Bigon travelled to Netherlands earlier this week to open talks with the Belgium international and they are hopeful that a €10m offer will be enough to lure Mertens to the Stadio San Paolo.
The 26-year-old is under contract with his current club until June 2016.