The former Rangers manager, speaking exclusively to Football Insider, insisted the Hoops would not want to risk losing the 29-year-old for “nothing” when his current terms expire in 2023.
As quoted by the Scottish Sun on Sunday (6 February), Postecoglou insisted contract talks with Rogic are “the last thing on my mind”.
The Australian boss went on to say “unless someone knocks on my door and says they want to go I’ll just let it roll.”
However, McLeish suggested the Parkhead top brass will have already opened discussions over a new deal for Rogic.
“You absolutely wouldn’t want to lose a player of that stature for nothing,” McLeish told Football Insider’s Russell Edge.
“There’s probably talks going on that we don’t know about and Tom’s comfortable in his dealings with the club and his agent.
“Unless there’s a master plan for him and he goes somewhere else at the end of his contract.
“But certainly, in the form that he’s in and the form that we’ve seen in the last couple of years, to think he’s only 29. He’s coming to the absolute peak of his career. He is not even there yet.
“He has got another two or three fantastic seasons ahead of him, with even more experience. His legs are still good and he is a very, very valuable player.”
Rogic has been a mainstay under Postecoglou, playing 33 times across all competitions.
He has a total of 255 appearances under his belt for the Bhoys to date.