Clarkson, 29, became an unrestricted free agent last night and can start talking to teams on Wednesday, though like all UFAs, he cannot sign a new deal until July 5.
In 48 games with the Devils this past season, Clarkson registered 15 goals and nine assists for 24 points, along with 78 penalty minutes.
The Toronto native has played in 426 career NHL regular-season games, all with the Devils, and has accumulated 97 goals and 73 assists for 170 points, and 770 penalty minutes.
Meanwhile, contract negotiations between the Devils and left wing Patrik Elias are ongoing, a source close to the situation told TFP.
While the Devils seem confident a deal can be ironed out, it's unclear if one will be finalized before July 5.