Meanwhile, Tottenham are expected to confirm the departure of chief football officer Scott Munn this week.
The Australian administrator, who joined Spurs in 2023, is understood to have left the north London club amid an internal reshuffle.
Munn was a key figure in the appointment of fellow Australian Postecoglou in June 2023.
Vinai Venkatesham started in his role as new chief executive last Monday, while executive director Donna Cullen left the club.
Munn’s exit is another significant change in what is gearing up to be a crucial summer for Tottenham ahead of next season.
In addition to their search for new men’s and women’s head coaches, Fabio Paratici, the club’s former managing director of football, is in talks over a return to the club once his Fifa ban for alleged financial irregularities linked to his time at Juventus expires in July.
The Italian has been working with Spurs on a consultancy basis during his suspension, with the process towards his permanent reappointment ongoing.
There has been interest from the Middle East in Paratici, but it is understood he is keen to rejoin Tottenham.
