They are already facing an injury headache, with key man Jota expected to be out until next year with a hamstring complaint.
Postecoglou wants to make sure he has the squad to compete across domestic competitions and the Europa Conference League.
Celtic have been heavily linked with moves for Japanese trio Daizen Maeda, Reo Hatate and Yosuke Ideguchi – but Postecoglou, who has already plucked Kyogo Furuhashi from Asia, says he is looking at players from less well-known leagues such as South Korea’s K-League and Iran’s Pro League.
When asked after the 3-0 win over Dundee United if he would be looking at the Far East for players, Postecoglou said: “I don’t want to say that! Because everyone will go there and start looking. I’m obviously at an advantage because I worked there. It would be silly of me not to use the experience I have and the knowledge I have.
“That’s why we got Kyogo here. I was 100 per cent certain he would do well. And it’s not just Kyogo. If you look at all the big leagues around the world, you’ll see Asian players.
“Not just from Japan but from Korea, from Australia, from Iran. There are some very good footballers on that side of the world. But if people don’t want to look there, I’m happy to be the only one.”