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.
I think everybody wanted the puck tonight. Everybody wanted to be part of the solution and it reflected on the way we played. It's tiring when you have to chase the puck but tonight was one of those nights where everyone really wanted to make a play and wanted to have an impact on the game.
— Rangers forward Martin St. Louis after a 2-0 win against the Flyers