The former Rangers manager, speaking exclusively to Football Insider, suggested a move for the 23-year-old would be proof of the Hoops’ faith in the Australian manager’s recruitment knowledge.
As reported by Football Scotland (3rd November), Celtic are in talks to sign Hatate either for a nominal fee or on a free transfer.
The versatile midfielder is out of contract at the end of January.
He has played a starring role for Kawasaki in winning the J-League title and Japanese Super Cup this season.
Postecoglou, who joined Celtic from Yokohama F. Marinos, returned to Japan for the signing of Kyogo Furuhashi in the summer.
McLeish insisted every manager wants to feel supported by their board.
He insisted the prospective capture of Hatate would demonstrate the backing Postecoglou has from the Parkhead hierarchy.
Asked if a move for Hatate proved Celtic’s faith and belief in the manager, McLeish told Football Insider’s Russell Edge: “Yeah. There’s no doubt about that.
“When you’re a manager you need to have a good relationship with the men above you.
“The one thing that every manager craves is to get support from above. That is both financially and sometimes when it’s a rainy day.
“Any time I’ve had great rapport and leadership from people above, I’ve had relative success.”
Hatate has been utilised in several positions by Kawasaki but has featured predomoninantly as a midfielder this term.
However, he started the season playing at left-back and has also operated as a winger on occasion.