The Australian suffered his first Premier League defeat in a 4-1 loss to Chelsea on Monday, where Destiny Udogie and Cristian Romero were both banished from the field either side of the break.
While Udogie only has to serve a one-game ban, Romero's straight red means that the Argentine will sit out three matches, also rendering him unavailable for meetings with Aston Villa and champions Manchester City following the international break.
In addition, Micky van de Ven (thigh) and James Maddison (ankle) were taken off during first-half injury time on Monday, joining Ben Davies (ankle), Manor Solomon (knee), Ivan Perisic (knee), Ryan Sessegnon (thigh) and Alfie Whiteman (ankle) in the infirmary.
Postecoglou has conceded that Van de Ven's issue looks to be severe, leaving Eric Dier as Spurs' only senior central option for the trip to Molineux, and the Englishman is therefore guaranteed a first Premier League start of the season alongside Guglielmo Vicario and Pedro Porro.
Much will hinge on Davies's fitness regarding Postecoglou's other defensive choices, as the Welshman would be a straight swap for Udogie on the left, allowing Emerson Royal to operate as an emergency centre-back.
However, should Davies not make the cut, Emerson would likely deputise for Udogie out wide, potentially forcing Postecoglou to take a punt on 18-year-old Ashley Phillips alongside Dier, although Pierre-Emile Hojbjerg was deployed in the heart of defence for the second half on Monday evening.
Yves Bissouma and Pape Sarr's midfield partnership will not be impacted by Spurs' wealth of absentees, while there is hope that Maddison will recover from his ankle concern in time to play a part on Saturday.
Richarlison - who was dropped to the bench versus Chelsea - has also announced that he will soon go under the knife to treat a pelvic injury, so Brennan Johnson ought to hold his position alongside Dejan Kulusevski and Son Heung-min in attack.
Tottenham Hotspur possible starting lineup: Vicario; Porro, Dier, Phillips, Royal; Sarr, Bissouma; Kulusevski, Maddison, Johnson; Son