QPR have made their interest in the 20-year-old official, with a £460,000 bid reported to have been lodged.
Last week, Reading had a £400,000 offer accepted by Rogic's club, Central Coast Mariners, but the midfielder chose not to make the move.
With other clubs still in the hunt, the Hoops believe they are still ahead of the chasing pack as they have Rogic training with their squad here in Marbella.
With Neil Lennon back in Britain attending a managers' and coaches' seminar at the FA's St George's Centre, Celtic want to bring Rogic with them when the squad heads back to Glasgow on Wednesday.
But with the star now free of his three-game domestic suspension and available for Mariners' A-League game this weekend, that plan will only be given the green light if Celtic upgrade their interest to 'formal' by talking money.
Mariners chairman Peter Turnbull said: "Celtic appear to have been impressed with Tom during his stay in Spain, and have requested Tom travel back to Glasgow with them to view their facilities, and see Glasgow first-hand.
"It's not surprising to see Tom in such demand, and from such big clubs.
"We're proud to have been able to give Tom this opportunity, and are especially pleased to see the quality of the clubs that have shown interest."