The Hoops boss is now assembling his team for the upcoming season and has recently signed Aaron Mooy on a free transfer and Moritz Jenz on loan from French team Lorient.
Moreover, Cameron Carter-Vickers and Jota, both of whom played the previous season on loan at Celtic Park, made their moves permanent this summer.
The Bhoys manager insisted that the club will be alert in the remaining weeks of the transfer window and stressed that if they decide to make a move for a player, then it must be the right one.
Postecoglou is of the view that last season the Hoops squad got a bit stretched due to injuries and a lack of depth, which they are determined to address in the ongoing transfer window.
“We always want to fill in some gaps that I felt we had in the squad last year”, Postecoglou told Sky Sports Scotland.
“The areas we got stretched in.
“We had some significant injuries because we just didn’t have the quality of depth needed.
“We have looked to address that this year.
“It is fair to say we will still be active.
“Whether we get deals done is another thing; it’s got to be right ones.
“We expect there to be some comings and goings over the next couple of weeks while the window is open
“Without putting any certainty around it, we will be alert and ready to go if the right solution comes.”
The Hoops are undefeated in their last five friendly games, and will face Championship side Norwich City next before they begin their Scottish Premiership campaign against Aberdeen on 31st July.