A team executive confirmed that the Bolts were dangling Malone as bait last season.
It's believed Lightning GM Steve Yzerman will look to deal Malone at some point this season, but it's unclear what he would be looking for in return.
Malone, 33, has two-years left on his contract, including this season. He's set to earn $2.5 million each year (his contract will be pro-rated this season as a result of the 48-game schedule put in place due to the lockout), though his salary cap hit is $4.5 million.
The Los Angeles Kings and Pittsburgh Penguins were among the teams that showed some interest in Malone last season.
Malone began his NHL career with the Penguins, playing four seasons in his native Pittsburgh, before his rights, along with Gary Roberts' rights, were traded to Tampa Bay on June 28, 2008 for a 2009 conditional draft pick. He signed a seven-year deal with the Lightning two days later.
While he would have had to sign off on any trade the Lightning tried to make last season, he must now list up to 12 teams he would accept a trade to, according to Capgeek.com, and would need to give his blessing on any deal made outside that list.
In 68 games with the Lightning last season, Malone registered 20 goals and 28 assists for 48 points, along with 82 penalty minutes.