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.
Once again, it shows character in this dressing room. Once again, there's no quitting in here. We all wanted this so bad and we worked so hard to get home-ice advantage and we weren't going to let this one slide.
— Colorado Avalanche captain Gabriel Landeskog on his team's OT Game 1 win vs. Minnesota Wild