The Australia international, who has been missing for two months with a knee problem, was an unused substitute for Saturday's 3-2 win over Partick Thistle in the Scottish Cup.
Rogic was expected to get game time in Celtic's Under-20s match against Motherwell on Monday at Morton's Cappielow Park, but adverse weather forced the game to be cancelled.
"Tom's a little bit further on [than some of the other injured players] in that he's had a couple of weeks' training and he's going to be hopefully available in a week or so," Davies told the Daily Record.
"Ideally there was a development game he was going to play in because he needs to get some minutes. That's usually the process players go through on their return. He's had some good training and he's on his way back from being out for a while."