ble."Williams, 29, has just over a year left on his existing Swansea contract and Italian heavyweights Napoli - the Swans' Europa League conquerors this season - are among those thought to be tracking him.
"What he does for the club, I would have him here for as long as possible," Swansea head coach 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 will be an integral part of Swansea's plan to beat title-chasing Chelsea at the Liberty Stadium on Sunday, when a win for Monk's men would effectively erase any lingering relegation fears.
The game comes just five days after Chelsea booked a Champions League semi-final place by knocking out Paris St Germain, and Monk is fully aware of the challenge that awaits.
"I don't buy we could catch them cold after midweek," he added.
"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.
"The journey this club (Swansea) has been on and fighting for is to be on this level, to compete against these sort of teams, and we have to make sure we continue that."
Swansea will go into the Chelsea clash following a 1-0 defeat to Hull last weekend, which came as a jolt, given that Monk had seen his team draw with Arsenal and beat Norwich in their previous two games.
Swansea are currently six points above the relegation zone
After Chelsea, their remaining fixtures are against Newcastle, Aston Villa, Southampton and Sunderland.
"I was very annoyed with the (Hull) performance
The training was very good, the sessions very competitive," Monk said.
"As a manager all you can do is get it to that level and understand fully what is expected that they do it on a Saturday
That's the disappointment - the work they put in and we end up with a performance like that.
"If you had to say mathematically, we need two more wins
I want it, and we're aware of it
But we want more, we want consistency
We have been too inconsistent this season.
"It is not as if it is small inconsistencies
We have performed brilliantly, then against Hull we were very, very poor.
"It is too big a gap
The best teams stay at a level, and that is what I want for the rest of the season."
Source : PA
Source: PA