The Bhoys have already signed defenders Liam Shaw and Osaze Urhoghide as well as wingers Liel Abada and Kyogo Furuhashi this summer.
However, Postecoglou insists the club are still looking to strengthen their squad in order to reclaim the Scottish title after Steven Gerrard led Rangers’ championship-winning campaign last term.
“It’s a very young group at the moment that we’re throwing out there,” the former Australia national teram coach told Celtic TV. “It’s no secret that we need to bring some players in and we’re working hard to do that.
Celtic host Danish club Midtjylland in the first leg of their Champions League second qualifying round tie on Tuesday.