The deal is reportedly worth $1.5 million, a source told ESPN.com's Pierre LeBrun.
Bouillon, 37, has one goals and six assists in 28 games this season. He joined the Habs for a second time as a free agent in 2012. He also played for the Canadiens between 1999 and 2009.
Bouillon has scored 30 goals and added 11 assists in 704 regular season games with Montreal and Nashville, with 489 penalty minutes through his career.