The 29-year-old defender 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 reported to be tracking him.
"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 that he can take on to the pitch to influence the rest of the guys."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball