Williams turns 31 in August and signed a new four-year Swansea deal last summer but television pundit Robbie Savage claimed last weekend that the Wales captain should be playing for a top-six club.
Those comments did not go down well with Monk who says Williams stands for the values at Swansea and is integral to the club's future.
"Ash is massive for us and I think he's been linked every year near enough to moving away," Monk said ahead of Swansea's Barclays Premier League trip to Tottenham on Wednesday.
"It was important that he signed a new long-term contract for the club last summer.
"He's very settled here and loves the club.
"He stands for a lot of what we are doing and how I want to go forward with the club and the team, so I don't envisage that changing at all."
Monk lost top goalscorer Wilfried Bony to Manchester City in January as Swansea accepted a deal which could rise to £28million for the Ivorian.
But Monk is adamant Swansea are not under any pressure to sell players and his focus this summer is on adding quality to his squad.
"Ever since we've been in the Premier League so many of our players have been linked with this club or that club," Monk said.
"Of course, there will be players that come and go every single season but the good thing is that is dictated by us.
"We're under no pressure to sell and we don't need the money
"We want to add quality to the squad and not take it away and luckily we're in a good position to do that."
Swansea could come up against former favourites Michel Vorm and Ben Davies at White Hart Lane, although neither player has been able to establish themselves at Spurs since summer moves.
Dutch goalkeeper Vorm has been very much Hugo Lloris' understudy while Wales defender Davies has made only seven league starts in being second-choice to Danny Rose for the left-back spot.
"This is the difficulty always when you go to the bigger clubs," said Monk, who is expected to start his Tottenham old boys Gylfi Sigurdsson and Kyle Naughton
"They have bigger squads, the depth of quality and competition is a lot more and they're fighting for their places."
Source : PA
Source: PA