Butler, 26, split the 2012-13 season between the Predators and New Jersey Devils, combining to total four goals and 11 points in 34 games. Butler previously played three seasons with the Ottawa Senators.
Brennan, 24, split last season between the Panthers and Buffalo Sabres, combining to total three goals and 10 points in 29 games. Brennan was a second-round pick by the Sabres in the 2007 NHL Draft.
Each player can become a restricted free agent this summer.
It's really exciting. I'm pretty sure that when I play my first game I'm going to be emotional. To be back on the ice playing a game, being in game situations, with all the routines and rituals I do before games and during the game, I feel like I'm going to be emotional. I'm going to be really happy.
— Canadiens forward Tim Bozon on playing for the first time since his life-threatening illness