The Swans, and Lions, have both refuted the report, with speculation around Franklin's future only growing in recent days.
Franklin's famous nine-year deal with the Swans concludes this year, with the four-time Coleman Medal winner a restricted free agent at the cessation of this season.
Sydney have expressed their confidence in re-signing their superstar veteran beyond this year, however Franklin has revealed he is yet to make a decision as he weighs up what's best for his family.
A statement released through his manager Adam Finch detailed that contract talks have been halted ahead of the off-season, via AFL Media's Cal Twomey.
“At this stage conversations have been paused around my contract so I can put all my focus on playing footy. No further comment will be made until the season is done & I have decided about my future," the statement reads.
“I am still undecided and need time after the season to make a family decision about whether I continue to play next year.” 2/2 👀
— Callum Twomey (@CalTwomey) August 5, 2022
“I am still undecided and need time after the season to make a family decision about whether I continue to play next year.”
Links connecting Franklin to the Lions came after he and his partner Jesinta bought a house in Queensland, hoping to be closer to family on the Gold Coast.
Recent reports have also suggested Franklin turned down an extension offer from the Swans in the vicinity of $500,000 per season to play in 2023.
Speaking to 7 News, Sydney chairman Andrew Pridham said the club are in no rush to reach an outcome with Franklin over his future.
“We are very supportive of Lance putting off making a decision on his contract until post-season,” he said.
“It is an important decision for Lance, his family and the club. I see no need to rush an outcome.”