It’s understood that Rogic, just back from a 10-week injury absence, was unimpressed by the terms on offer and coupled with a squeeze on game time this season, and the arrival of fellow midfielder Charly Musonda on an 18-month loan from Chelsea, is now contemplating his Celtic Park exit strategy.
The gifted, yet sometimes enigmatic 25-year-old, has been unable to produce his most compelling form this season, making 29 appearances - 13 of those off the bench - in all competitions. He has scored four goals.
Currently valued at around $6 million, Rogic has 15 months remaining on the three-year contract extension he signed in mid-2016.
He joined the Hoops in 2013 from Central Coast Mariners, and after an injury plagued couple of years banged in 15 goals in 52 league appearances over the past two seasons.
But it’s been a different story so far in 2017-18, with a knee injury stopping him in his tracks and coach Brendan Rodgers appearing less enamored with a player capable of the spectacular but with question marks over his durability over 90 high-tempo minutes.
Leeds United tried to sign Rogic just before he inked his current deal, and he’s previously been linked with Arsenal, although that claim was viewed by many as fanciful.
Rogic, who came off the bench as Celtic crashed out of the UEFA Europa League against Zenit Saint Petersburg on Friday (AEDT), has scored seven goals in 33 appearances for Australia.
And, in the light of his decision to knock back a new deal, he will be hoping to attract suitors with some stellar performances for his country at the World Cup in Russia in just under four months time.
If further talks don’t eventuate, Celtic could opt to cash in on Rogic in the northern summer, rather than let him go for a token fee, or for free, as his existing deal winds down.
The fan-favourite scored a stunning late winner against Aberdeen to seal Scottish Cup glory and a Treble for Rodgers’ Invincibles.
But he hasn’t hit the net this season since firing the opener in the 2-0 victory over Rangers at Ibrox on September 23.