Postecoglou has reportedly agreed a two-year contract with Tottenham after leading Celtic to the treble in Scotland this season.
The Australian had dodged questions on his future before and after Celtic's Scottish Cup final win over Inverness on Saturday.
Tottenham are desperate to find a new boss after a dismal season in the Premier League climaxed with failed attempts to hire Feyenoord manager Arne Slot and former Bayern Munich coach Julian Nagelsmann.
Neither club are commenting publicly but reports claim Postecoglou told Celtic principal shareholder Dermot Desmond on Saturday that he plans to join the north London club.
Speaking after the Scottish Cup final, Greek-born former Australia boss Postecoglou said: "I anticipate enjoying this moment for the next 24-48 hours, as long as I can, before someone drags me away and takes my attention away from enjoying something that's been hard-earned.
"The reality is, there's probably players in that dressing room who won't be here next year. That's the nature of football.
"But I want them to enjoy it, I am going to enjoy it, and that's all I am going to focus on until someone grabs me by the collar and tells me that I have to answer certain questions."
Postecoglou has won five domestic trophies, including successive league titles, since arriving at Celtic from Japan's Yokohama F Marinos in 2021.
Postecoglou became popular with the Celtic fanbase, not just for resuming their success after a barren season, but also for implementing an attacking style of play.
But now he looks set to swap Glasgow for another rebuilding job as Tottenham finally hope to appoint a permanent successor to Antonio Conte, who departed by mutual consent on March 26.
Postecoglou is due to go on a family holiday on Tuesday and a deal could be finalised imminently.
Tottenham finished eighth in the Premier League after a troubled campaign that saw Conte label the players "selfish", while criticising the culture of a club that last won silverware in 2008.
Conte's interim successor Cristian Stellini was quickly sacked after a wretched run, leaving Ryan Mason to take charge on a caretaker basis until the end of the season.
Amid a toxic atmosphere in the stands throughout the season, fans called for Tottenham chairman Daniel Levy to quit and protested against club owners ENIC.
Tottenham's all-time leading scorer Harry Kane could be sold in the close season, with Manchester United and Real Madrid said to be interested in the England captain, who has only one year left on his contract.
