With just one year to go on his existing contract, the Wales international is expected to court interest in the summer transfer window.
Napoli are among those reportedly interested in the 29-year-old, while Arsenal have been linked with the centre-back in recent years, but Monk is hopeful on keeping his skipper in South Wales for "as long as possible".
He told reporters: "What he does for the club, I would have him here for as long as possible."
"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."
The Swans host Premier League title challengers Chelsea on Sunday afternoon, kickoff for which is scheduled for 4.07pm.