The midfielder recently opened talks with the Hoops regarding a fresh deal with some reports suggesting he may ask for a big pay rise to remain at Parkhead or move on for more cash.
But Coleman believes his Dragons middleman will stay put in Glasgow and continue improving his game with Scottish champions.
"Listen, right now Joe's playing for Celtic. It's a huge club," Coleman told SunSport.
"They have had a really good run in Europe, they're going to win the league and he's enjoying his football.
"He has improved as a player since he's been at Parkhead and that is the main thing.
"I wouldn't be surprised at all if he signs another contract there.
"Guys who move for the quick buck don't tend to last too long.
"The guys who are in it longer do so because they're in it for all the right reasons.
"Don't get me wrong, if someone puts a big contract in front of you you're definitely going to sign it - but just as long as you're doing it for the right reasons. Joe's been around for long enough.
"He did a fine job for Cardiff, has been at Celtic for a while and is still playing well and winning things.
"That tells you he's in it for the right reasons."