The Napoli boss has been left impressed by Williams after Swansea's Europa League encounter against the Italian side, and is looking to strengthen his back-line with a bid in the summer.
Arsenal, Tottenham, Everton and Liverpool have all been linked with the 29-year-old Swans centre-back, although Brendan Rodgers was thought to be leading the race.
He worked with Williams during his time at Swansea, and the Liverpool boss was believed to be considering a bid at the end of the season.
Williams has just one more season remaining on his contract in south Wales, and could be tempted by a spell in Serie A.
But the ball-playing centre-back will probably have options closer to home, with Rodgers and Arsene Wenger reportedly big fans of the player.
Aston Villa have also been credited with an interest in the commanding defender.
Liverpool have plenty of options in defence, with Rodgers able to call on the likes of Mamadou Sakho, Kolo Toure, Daniel Agger and Martin Skrtel.
Arsenal, in contrast, could have a more pressing need come the end of the season, with Johan Djourou likely to leave permanently and Thomas Vermaelen agitating for first-team football.