The Parkhead side opened the transfer window with a bang last week with the triple signing of Japanese trio Reo Hatate, Daizen Maeda and Yosuke Ideguchi.
Celtic are also attempting to negotiate permanent moves for loan pair Cameron Carter-Vickers and Jota from Tottenham and Benfica respectively.
Further ins and outs are possible with Postecoglou promising to "stay alert" to potential moves for the remainder of the month.
"Not too busy but we've got to stay agile through this period," he told Celtic TV.
"We've had a couple of players go out on loan which I think is also important.
"We're looking at the squad the whole time and through the whole January window we'll make sure that, what we need, if it's available, we'll bring in. Also with the existing squad make sure that we're continuing to develop our footballers.
"I don't expect it to be too hectic but we'll stay alert and make sure that if the right thing comes along both in terms of incomings and outgoings we'll be able to move."