The Predators cannot speak with Stevens until the Kings' season is over, though the paper notes other teams, including the Vancouver Canucks, could be eyeing Stevens.
Texas Stars head coach Willie Desjardins and Grand Rapids Griffins coach Jeff Blashill are also being considered.
The Tennessean notes Blashill may be a prime candidate for the coaching vacancy.
Phil Housley, currently an assistant coach with the Preds, is also believed to be in the running.
Predators GM David Poile may also wait until the fates of Toronto Maple Leafs coach Randy Carlyle, San Jose Sharks coach Todd McLellan and Pittsburgh Penguins coach Dan Bylsma's futures are firmed up. If any become available, Poile is expected to inquire.