A media release from the Mariners said no bid had been tabled for the playmaker, but the Scottish champions will assess Rogic's suitability in the trial.
Rogic will take part in training with the Glasgow club, as well as undergoing sports science and fitness testing, before returning to the Mariners on January 17, two days before their A-League clash against the Newcastle Jets.
Central Coast manager Lawrie McKinna said the experience will be a rewarding one for the young Socceroo.
"This is a great opportunity for Tomas to train with Celtic's first-team squad," he said.
"Celtic are in their mid-season break and are busy preparing for their Champions League matches against Juventus starting in February, so Tom will undoubtedly learn a lot from the experience."