The 34-year-old goalkeeper signed on a three-year deal from Tottenham on Tuesday and immediately flew with the Hoops squad to the Czech Republic for the first leg of the Europa League third qualifying round tie.
Midfielder James McCarthy also signed on a four-year deal after leaving Crystal Palace at the end of last season but he is not yet up to speed.
The Celtic boss started the season with Vasilis Barkas in goal but he has been replaced by Scott Bain.
Hart could come straight in as the new number one but Postecoglou revealed he has not yet reached a decision.
"In terms of Thursday, we'll have a look at it. He only literally met the team last evening," he said.
"He has been training though. He's presented in good condition. He'll have his first training session with the team this afternoon. I'll make a decision after that.
"Look, I wouldn't gave brought him in if I did not think he could contribute to the team.
"With Scotty and Barky in particular, I just think they had a really tough year last year.
"Having someone like Joe around will help them as well because he's a player who's played at the highest level for a long time, he's experienced the ups and downs of football and I think having an experienced player like him around will also assist those two.
"The difference with James was he wasn't training at a club. He's been training on his own whereas Joe was training with Tottenham.
"So we made a decision to leave (McCarthy) back in Glasgow. He'll have a session today and tomorrow with our staff there and we'll have a look at him on Saturday.
"He's been working hard on his own and is keen to get started."
Celtic will also once again be without striker Leigh Griffiths, who is trying to get back up to speed following a knock.
Postecoglou has failed to win any of his first three competitive games in charge and is keen to get off the mark.
The Hoops were knocked out of the Champions League qualifiers by Danish side Midtjylland and lost 2-1 to Hearts at Tynecastle in their cinch Premiership opener at Tynecastle on Saturday night.
The former Australia boss is expecting a "tough game" against Jablonec and said: "Czech teams are always pretty well-organised, they are a big side, a physical side and I expect it to be a tough challenge.
"Every time you play away in Europe there are always unique circumstances you need to overcome and I am sure that will be the case for us. But we will try to maintain our focus on ourselves at the moment.
"Our football has been okay, it hasn't been brilliant, but it has been okay. We have had chances to win all the games so there is a real focus to keep improving but more importantly turning them into results."