Monk wants Williams 'as long as possible'
Williams' agent Peter Smith admitted this week that the 29-year-old central defender would be interested in speaking to Napoli coach Rafael Benitez, although maintained no contact had been made as yet.
Monk conceded on Saturday that he has not spoken to Williams about the Wales international's future with Swansea but made it clear he wants the skipper to stay at the Liberty Stadium.
"What he does for the club, I would have him here for as long as possible," Monk said.
"He has been linked with clubs for a few years - it is what happens with good players. He's an important player that, as a club, we should keep as long as possible.
"He is a good guy who cares for the club and wants the best for us. I know he is happy here and I don't see a problem.
"I haven't had a conversation about his future. I speak to him frequently but it's about the football, things we can improve and the defensive side of things, giving him things what he can take on to the pitch to influence the rest of the guys."
Williams' contract with Swansea will expire at the end of next season.
Since joining Swansea on loan in March 2008 - the move became permanent two months later - Williams has played 273 matches for the Welsh club.
Swansea will host Chelsea on Sunday desperate for some points as they continue to battle relegation.
Monk's men sit just three points and three spots outside the relegation zone with five games left this season.
Chelsea pulled off an impressive comeback against Paris Saint-Germain on Tuesday to reach the semi-finals of the UEFA Champions League but Monk still expects the London-based club to be focused.
"I don't buy we could catch them cold after midweek," Monk said.
"The players they have through the squad are top-class players. I am sure they will make changes but whoever comes in is top-class.
"They are not pushing for the title for no reason. They have experience and class all over the pitch. It's an extremely tough game but a challenge we are looking forward to and have to relish."