It's claimed Bruce will be dumped and replaced by former Tottenham boss Mauricio Pochettino.
"If they don't feel he's the man they want to take them to where they want to go then they have every right to change the manager," Carragher said on Sky Sports' Football Show.
"The new owners can't be criticised for doing that. (Mauricio) Pochettino is the best manager they could get at the moment. He's available but he is also getting linked with bigger jobs like Manchester Untied and Real Madrid at the moment."