Irvine, who parted company with relegated Championship side Hull City in June, will link up with Australia teammate Martin Boyle at the high-flying Scottish Premiership club if the move goes ahead.
The Daily Record claims a deal is close to being finalised to bring Irvine, 27, back to the country where his career initially unfolded, first at Celtic and then on loan at Kilmarnock and Ross County.
He moved to the latter on a permanent deal before being snapped up a year later by then Championship club Burton Albion.
Irvine is expected to undergo a medical imminently as he prepares to dust off the cobwebs of his long sabbatical.
Irvine’s last competitive match was Hull's 5-1 pre-COVID Championship loss to Stoke City on March 8.
He went on to make 107 league appearances across three seasons for the Hull.
Easter Road was also recently home to fellow Australians Mark Milligan and Jamie Maclaren, with a resolution to Irvine’s predicament sure to bring relief to Socceroos coach Graham Arnold who has been hoping he gets up and running again prior to March’s planned resumption of Australia’s 2022 FIFA World Cup qualification campaign.