The Socceroos midfielder was supposed to travel to the Middle East this week for advanced talks but now appears to be having second-thoughts, according to SunSport.
It is believed the lower-profile league is perhaps a step too far for the 27-year-old, who could yet hold out for another European club.
Rogic, a peripheral figure at the Scottish champions, still has three years left on his contract at Parkhead, where manager Neil Lennon has helped sustain the Hoops' domestic dominance.
Celtic are aiming for their 10th straight Scottish Premiership title this season, but will face stiff competition from arch-rivals Rangers once again.
Whether Rogic remains a part of those plans, however, remains to be seen.
