Franklin's future has been highly speculated in recent weeks after reports emerged of an extension at Sydney was turned down by the 35-year-old.
According to Nine News, the Lions are Franklin's preferred destination in departing the Swans, looking to move his family north.
"[Franklin]'s future has been a hot topic in AFL circles and I can confirm tonight that the Brisbane Lions are currently the front-runner to be his club next year," Nine News' Michael Atkinson reported on Thursday night.
"It's my understanding that Franklin has informed the Swans that he won't be playing in Sydney next year.
"Franklin and his wife Jesinta have a desire to move their family up to Queensland to be closer to family on the Gold Coast. But it's not the Suns where he wants to keep playing, Buddy wants to win more premierships and he's identified Brisbane as the club most likely to help him achieve that goal.
— 9News Queensland (@9NewsQueensland) August 4, 2022
"It's my understanding that Franklin's management and Brisbane Lions bosses have held talks already, albeit at this stage they're just preliminary conversations.
"There's a lot of water that still needs to go under this bridge... but right now the Lions are the front-runner the land Buddy Franklin."
Franklin has played 153 games for Sydney since switching from Hawthorn at the end of the 2013 season, having won two premierships as a Hawk.
The Western Australian has won eight All-Australian selections, 12 club leading goalkicker awards and four Coleman Medals across 335 AFL matches.