The Hoops are seeking a new manager after Brendan Rodgers resigned on Monday.
Rodgers chose to quit after the defeat to Hearts on the weekend.
Celtic have installed Martin O'Neill and Shaun Maloney as caretaker managers.
The Daily Mail says Postecoglou, just a fortnight after his dismissal by Nottingham Forest, is being mentioned among candidates for the Celtic post.
Postecoglou won back-to-back Scottish League titles with Celtic and the domestic treble in 2022/23 before moving to Tottenham.