The former Yokohama Marinos head coach quickly secured the signing of Kyogo Furuhashi after arriving in Glasgow and the Japan forward has netted six goals in his first five starts.
Postecoglou cautioned that there was nobody else quite like his new striker in Japanese football, but there are other targets he would like to explore.
"I have been looking at it very closely," the Greek-born Australian said. "I know the Japanese market very well.
"It's a tricky time because traditionally they are still mid-season. There's a lot of players I would love to have a look at closely and bring over but I know it would be almost impossible to get them out because clubs are still playing for the league or cup or (AFC) Champions League competitions. So they are very reluctant to let them go mid-season.
"Traditionally it's always been easier to get them out in our winter break, which is their end of season.
"There's a lot of talent there that people haven't realised.
"It's not to say they are all going to be of Kyogo's level because I was super confident about him. He has dominated that league for the last three or four years. I was surprised he hadn't left earlier to be honest, we were kind of lucky he stuck around for a bit.
"But there is definitely more talent there and it is definitely a market we are looking at closely."
Celtic are still working on more pressing transfer deals, with Legia Warsaw right-back Josip Juranovic and Shamrock Rovers centre-back Liam Scales expected to arrive shortly.
VVV-Venlo have also confirmed that Celtic are interested in their striker, Georgios Giakoumakis, who was the top goalscorer in the Eredivisie last season.
Postecoglou said: "Obviously the clock is ticking, we know when the transfer deadline is and we will be bringing in players before then but we can't say another deal has been done.
"But we are close on a number and hopefully over the coming days we will be able to bed them down and bring them in."
Postecoglou will be able to relieve some of the pressure on the players who featured in Wednesday's Europa League win over AZ Alkmaar with Ryan Christie back in the squad after injury.
Postecoglou will wait to assess who needs a rest most but he is confident there will be no slacking for Saturday's cinch Premiership contest with St Mirren at Parkhead, ahead of next week's second leg in the Netherlands and a trip to Ibrox.
"I would be very surprised if anyone is taking anything for granted," said Postecoglou.
"The world, and the football world in particular, changes pretty quickly and once you take something for granted you will get brought back to earth.
"Look, I haven't sensed that at all with this group. The key thing for us is that they are enjoying their football, they are getting their rewards, and for the most part none of them want to miss out.
"That's a good thing for me but it's also part of the battle, when I ask them how they are feeling they are all buzzing and all want to play but I know there must be a couple who feel a bit sore.
"But when you have that sort of attitude and enthusiasm, it's unlikely they are going to be going in there looking for an easy game. I think they are going in there looking to play our football, improve our football, and make sure we don't stand still at any moment."