Franklin has been seen as likely to call time on his decorated career at the conclusion of this season - the 36-year-old's 19th campaign in the top flight.
The four-time Coleman Medal winner penned a one-year extension at the end of last year to see out 2023 in the red and white after his famous nine-year, $10 million deal came to a close.
The club's announcement at the time came with a short statement from Franklin: "One more", hinting the additional 12 months could be the 1,000-goal great's last in the AFL.
According to The Herald Sun, Franklin had informed close friends and family that this year would be his last, however the veteran sharpshooter is understood to be open to potentially extending his career for another season.
It is understood that Franklin's initial plan to hang up the boots after over 350 games came amid a battle with form, with the Sydney forward held goalless in four matches across a six-game period before managing to rekindle his best efforts in recent weeks.
Franklin has kicked multiple majors in his four games since last going without a goal, including a haul of three against Fremantle last Saturday as the spearhead in John Longmire's attack for a must-win encounter.
The Herald Sun's report suggests an "open-minded" and "refreshed" Franklin is now pondering whether he could play on for a 20th season. It is not specified whether another campaign would come in Sydney or elsewhere.
Sydney would also need to be open to re-signing their seven-time leading goalkicker, who has played an integral role in aiding the development of emerging tall forwards Logan McDonald, Hayden McLean and Joel Amartey in recent years.
The Swans could see the fledgling trio as a priority ahead of Franklin in their pursuit for another premiership, with both McDonald and Amartey signed up for the future and McLean currently in discussions over a new deal.
Franklin has played 171 games and booted 486 goals with Sydney since making the highly-documented switch from Hawthorn at the end of the 2013 season.
Sydney are currently seen as outsiders to make the finals this year despite a grand final finish last September, with Franklin potentially facing the final five weeks of his career if he is to choose to retire at the cessation of this year.