The Chicago Blackhawks have also shown interest in the 34-year-old, another source told LeBrun.
Perry is not the top-tier scorer that he used to be, but he's still capable of producing when healthy. The veteran winger tallied 19 and 17 goals during the 2016-17 and 2017-18 seasons, respectively, as a member of the Anaheim Ducks.
The Predators scored the third-fewest goals among all playoff teams this past season and could benefit from the offensive upside that Perry supplies on the wing. The 2011 Hart Trophy winner could also provide the Predators with another option for a dismal power-play unit that ranked last in the NHL a season ago.
Scoring isn't the Blackhawks' problem these days, but with $16.2 million in projected cap space, adding another offensive threat to a skilled forward group could be something they consider.
Perry was bought out by the Ducks on Wednesday after spending the first 14 years of his career with the team. In a franchise-record 988 career games, Perry recorded 372 goals and 776 points.