The club want to bring back the hugely popular winger they sold to Saudi Arabia side Al-Faisaly for £3million earlier this year.
Despite Boyle’s arrival, the club were relegated to the second tier even though they progressed in the AFC Champions League.
As part of the deal, the club have a first refusal option which means they are notified of any bid for Boyle, giving them a chance to match or better the offer.
The move to Saudi Arabia was life-changing for the player and his family with the money on offer. Al-Faisaly’s new season in the 18-team Saudi First Division League starts later this month.
Boyle, a Scottish Cup winner with Hibs, will likely be part of the Australia squad for the World Cup in Qatar which starts in November having started the play-off against Peru to help the Socceroos reach the tournament finals.
When he left the club he left the door open for a return, tweeting “it’s not goodbye, it’s see you later”.
Last month Ron Gordon spoke about Boyle.
"The situation with Martin Boyle was one that we weren't looking to do but at the end of the day we want to support Martin,” he said.
"It was an opportunity for him to make some very good money, even if it hasn't turned out exactly the way he might have hoped.”