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.
He's only 17 but he can see the ice so well and he moves the puck and goes to the open ice all the time, so I just think he's a player that is ready to play in the NHL. I'm really looking forward to coaching someone like this.
— U.S. National Junior Team coach Ron Wilson on Auston Matthews, the projected No. 1 pick of the 2016 NHL Draft