The native of Sicamous, British Columbus, is believed to be looking for a significant raise, prompting trade speculation.
According to TSN Hockey Insider Darren Dreger, who reported this news via his Twitter account, the Leafs would prefer to keep Franson, but his asking price is too high.
Dreger suggests the Leafs could deal Franson for a prospect and a draft pick.
Several teams are looking to acquire a top-four defenseman, including the Edmonton Oilers, Carolina Hurricanes, Calgary Flames, Colorado Avalanche and Detroit Red Wings, and could connect with Leafs GM Dave Nonis about Franson's availability.
In 243 career NHL regular-season games with the Nashville Predators and Maple Leafs, Franson has accumulated 23 goals and 77 assists for 100 points, along with 76 penalty minutes, over four seasons.
He was originally drafted by the Predators in the third-round (79th overall) of the 2005 NHL Entry Draft.