The 30-year-old signed a new four-year with the Swans last summer, and one television pundit has claimed the Wales international should be playing for a top-six club.
But Monk dismissed those comments and is adamant the defender 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 the 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.
“Ever since we’ve been in the Premier League so many of our players have been linked with this club or that club.
“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.”