Postecoglou is believed to be the frontrunner to become the next Spurs boss and Celtic are believed to be resigned to watching him move south of the border at some point.
Levy is reportedly set to hold talks with the Australian on Monday following this weekend’s Scottish Cup final between Celtic and Inverness.
The 57-year-old is tipped to become the next Spurs manager if the talks go well with Levy.
But it has been claimed that the Tottenham chairman has not completely made up his mind about Postecoglou.
Former Barcelona and Spain boss Luis Enrique and Fulham manager Marco Silva are still in the running.
Levy wants to give his full consideration to all three names before making a final decision on the new Tottenham manager.
He has taken charge of the process and is being aided by the club’s chief football officer, Scott Munn.
Silva is in talks with Fulham over a new deal and it is unclear whether the Cottagers would be prepared to deal with Spurs if they make an approach for the Portuguese.
The compensation clause for the final year of his contract is said to be around £6m.