So far the Scottish champions have reinforced with the signings of left-back Alexandro Bernabei and goalkeeper Benjamin Siegrist, while Daizen Maeda, Cameron Carter-Vikcers and Jota have all signed permanently.
The club have been linked with a whole host of midfielders following the departures of Tom Rogic and Nir Bitton.
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Hide AdTwo of the latest names touted have been Paris Saint-Germain teenager Edouard Michut and Australian international Aaron Mooy.
The former is looking to leave the French giants in search of regular first-team football and the latter, who once had a spell at St Mirren, is a free agent.
Speaking to the press after Celtic’s 4-2 win over Banik Ostrava in the Czech Republic during pre-season, Postecoglou provided an update on where the club stand with both players.
He spoke of Michut being a good player but denied the club were interested.
As for Mooy, he said: “Aaron’s a fantastic footballer, somebody I know really well. I guess he’s getting linked with us.


“I’m sure he’ll get picked up, he’s a good player, a talented player.
“He’s another footballer who is very much talented and very much in my range. But, that doesn’t mean we’re going to bring him in, no.”
Meanwhile, Celtic continue to pursue St Mirren star Dylan Reid.
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Hide AdThe 17-year-old is one of the highest rated midfielders in Scotland and has already made his first-team breakthrough with the Buddies.
St Mirren boss Stephen Robinson is hopeful the club can show it is the best place for Reid’s development.
He was an unused substitute during the Premier Sports Cup opener with Arbroath. He made three Premiership appearances last season as well as spending time with Queen's Park on loan.
"Obviously we believe Dylan is a highly rated young talent that we can develop here," he told Sky Sports. "We are a club which produces players, an academy system which does develop players.
"For me it is a very good club for young players to develop.
"Dylan and his advisers and his family have some decisions to make but I don't think he needs to look too much further than here to develop."