Manager Neil Lennon is already convinced the 20-year-old is worth the £400,000 transfer fee which his A League club, Central Coast Mariners, are seeking.
Rogic only arrived at Celtic's training camp on the Costa Del Sol at Friday lunchtime after his flight from Australia was delayed.
With Lennon now back in Britain to join a stellar guest list at a dinner being hosted by Sir Alex Ferguson this evening, then attending meetings with the League Manager's group over the next few days, he will not get the chance to fully assess Rogic's abilities.
However, the need to move quickly is obvious as Reading, Fulham and QPR are among the clubs also in pursuit of the rising star.
Although Lennon will not be present at Tuesday's game against Steuaua Bucharest in Marbella, he hopes to persuade Mariners to allow Rogic to play in it.
The manager said: "We like the look of him. He's a nice mover with the ball and has a good left foot. We're hoping to get him back to Glasgow for another week to have a proper look."
With Rami Gershon already in on a six-month loan from Standard Liege, and serious interest confirmed in Chivas USA's Juan Agudelo and FC Ashdod's Juwon Oshaniwa, Celtic have made clear their intentions to tweak their squad in this window.
That could include moving out some fringe players, but Venezuelan striker, Miku, is not on Lennon's list for removal, even though his year-long loan from Getafe has not been a success.
A groin injury delayed him joining the rest of the squad in Spain, but Lennon insists he can still figure in his plans.
He said: "He's not had the impact yet, but it takes a bit of adjustment. He knows time is running out, but we want him to be a success here."