Celtic have completed the signing of Israel international winger Liel Abada on a five-year deal from Maccabi Petah Tikva.
And Postecoglou is confident more signings will arrive at Parkhead.
Postecoglou said: "We are trying to get some players in and hopefully get some deals done.
"We need some players to come in because we lost a fair few from last year. It is not an easy process at the moment, but we are pushing hard and hopefully we will get some in the next few days.
"I can't control who leaves, what I can control and push for is to bring people in."
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