The Hoops boss confirmed that he has been unsuccessful in his bid to sign a player he worked with during his time in charge of Australia after revealing the 23-year-old internationalist "decided to look elsewhere".
Postecoglou said: "McGree was someone I had an interest in because of my association with him and obviously I know the player pretty well.
"But after initial discussions he has decided to look elsewhere which is fine.
"But we've not spoken to one other player aside from the players we brought in."
Asked if he was expecting any other incomings this month, the former Australia manager said: "Unless something extraordinary comes along or something happens within the existing squad that means we need to move but as we speak right now there is no other offers or people I have spoken to.
"So the 20 names that come out tomorrow are all lies or fabrications or people bored at home just googling names and throwing them up there or agents trying to get a little bit of value for their client.
"I can't be any clearer than that. The one thing I won't do is lie.
"There is no one else we are talking to, there are no other offers, no one else I am showing interest in as we sit here today. If that changes I will let you know.”