New Lions coach Michael Voss revealed on Wednesday he was keen to speak to the delisted Davis to have a bona fide goalscoring alternative to twin towers Jonathan Brown and Daniel Bradshaw.
The mercurial 28-year-old played only three senior games for the Swans in 2008 due to indifferent early form and a season-ending knee injury.
Negotiations are at an early stage but Voss indicated the Lions were interested in picking Davis up through next month's pre-season draft.
"We've had a preliminary chat with Nick about perhaps the chance to come up here and train," Voss said.
"That is a distinct possibility.
"What we do have as a football team, we do have a need for that type of player so we're looking at all and every possibility of how we do that."
Davis was a proven match-winner for the Swans and key figure in their drive to the 2005 premiership, including a stirring role in a preliminary final comeback against Geelong.
Although his work ethic was questioned at the Swans and coach Paul Roos lost patience, Voss would welcome Davis' accuracy and creativity in front of goals in support of Brown and Bradshaw.
Voss also reiterated club chief executive Michael Bowers' sentiments that the Lions' door wasn't shut to former Eagles star Ben Cousins, but would give little else away about the club's plans in regard to the Brownlow Medallist.
"I think everyone knows what Ben Cousins' qualities are," he said. "From a football club side of things, there are obviously some other things we've got to consider at the same time.
"There are a number of things that have got to happen before we even get in front of Ben Cousins. First and foremost, Ben himself has got a number of things that he's got to overcome, so to me [that] is the priority".
Voss did indicate that he expected to be in contact with Cousins should the 30-year-old be cleared to pursue a comeback when the AFL Commission meets next Tuesday.
