Postecoglou has left the Bhoys to manage Tottenham Hotspur next season after guiding the Glasgow giants to win an unprecedented eighth domestic treble this term.
Following the Australian’s exit from Parkhead, the Celtic hierarchy have ramped up their search for a boss for next season.
And several managers have been linked with a move to the Hoops, including Rodgers, Graham Potter, Enzo Maresca and Kieran McKenna.
Rodgers was the early favourite to succeed Postecoglou at Parkhead, as the Northern Irish manager had a scintillating record at Celtic during his tenure at the Scottish giants between 2016 to 2019 when he won seven successive trophies with the club.
However, it is now claimed that the 50-year-old is increasingly unlikely to be at the helm of the Bhoys, albeit the prospect of his sensational return to Parkhead has yet to be dismissed.
Rodgers was relieved of his duties at now-relegated Leicester City in April and he was heavily linked with Spurs as the London outfit’s next manager.
It remains to be seen now whether Celtic rope in their former manager eventually or choose an option amongst those available on the table.