The midfielder is off contract in June and yet to be offered new terms by the Blues.
Wright told The Sun: "I think he will stay. Like I've said on so many occasions, Frank is a fantastic professional to have around your club.
"He's an inspirational character and everything you want about a professional at the minute, Frank has it.
"I find it very strange that Chelsea didn't sign him up before it got to the stage where he's now thinking about moving on. Why wouldn't you sign a player of that calibre who's ready to go again?
"You want young professionals to be looking at someone like him - Frank has done everything within the game at club level."