The 31-year-old has spent just one season in Brisbane after joining coach Chris Fagan at the Queensland club as a free agent.
The pair previously worked together at the Hawks, where Gunston was a key player in the club's hat-trick of premierships.
Gunston has one year left to run on his contract with Brisbane, who on Friday confirmed the player's desire to return to Hawthorn.
"While understanding Jack's situation, as a contracted player the club is assessing its position and will work through its options," the Lions said in a statement.
Gunston sensationally stepped away from Brisbane's senior side to complete a separate training block midway through this year.
He returned for rounds 17-22 but was overlooked at selection for the finals as the Lions ultimately fell four points short of Collingwood in a thrilling season decider.
In June, just before Gunston took his break, he questioned whether Brisbane's style of play suited his game.
"I played 12 years at Hawthorn and knew every mannerism, every way they (teammates) turned and kicked," he told the AFL website.
"I'm only 11 games in now and I'm still learning and working out which way guys turn and how they move and what type of kicks they do and look for.
"It's probably never going to be perfect, but we're slowly building the chemistry out there."
Jack Gunston (l) played his best footy in Victoria among his Hawthorn teammates.
Gunston, who turns 32 next week, started his career with Adelaide in 2010 before moving to Hawthorn, where he became an All-Australian (2018) and won a best-and-fairest award (2020).
The 242-game veteran led the Hawks' goal-kicking three times.
If Gunston returns to the club, he will again work under former premiership teammate Sam Mitchell, who is entering his third year as leader of Hawthorn's rebuild after taking over the coaching reins from Alastair Clarkson.
In other trade moves, Essendon have lodged paperwork to sign restricted free agent Jade Gresham from St Kilda.
The deal is expected to land the Saints a compensation draft pick at the end of the first round.
Fremantle are reportedly eyeing Collingwood's future first-round draft pick as part of a deal to grant energetic forward Lachie Schultz his trade wish to join the Magpies.
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