The club have now turned to their Plan B after primary target Eddie Howe turned down the job on Friday.
Parkhead chiefs are in advanced talks with the former Australian gaffer.
Mailsport understands that an offer has been made to Postecoglou and they are confident to have their man following positive discussions.
The 55-year-old has been on Celtic’s radar since Neil Lennon was dismissed as manager in February.
But they embarked on a long-term pursuit of Howe only to have the Englishman unplug the plug last week.
Postecoglou is now at the top of their list and the club hierarchy believe he will not be fazed by being their second choice.
Club sources confirmed last night that discussions were underway with him and his representatives.
And especially, Mailsport understands that Postecoglou is very keen to become Celtic’s new manager.
The club’s new CEO Dominic McKay sees this as an emergency and wants a deal to be done as quickly as possible, even though his target is currently in charge of Japan’s Yokohama Marinos team.
UK Covid rules could delay the appointment as Postecoglou is expected to quarantine for 10 days after arriving in the country.
But the Hoops are keen to make it as soon as possible after missing Howe.
Celtic next manager chase later
Postecoglou found success in the A-League Brisbane Roar squad and won the Asian Cup in 2015 as Socceroos boss.
And Celtic now believe he is the right man to replace Lennon as permanent boss as the club try to reclaim their Premiership title from Rangers next season.
They are in awe of his experience in the game and his coaching resume.
They also believe he is the strong personality type to handle the rebuilding of Parkhead’s squad this summer, with the future of several stars at the club uncertain.