Spurs make the long trek to Turkey aiming to maintain their 100% start to the 2024-25 competition, having already overcome Qarabag FK, Ferencvaros and AZ Alkmaar in the current edition.
With a perfect record of nine points from nine in the competition, Tottenham sit second in the 36-team Europa League standings, only training leaders Lazio by virtue of an inferior goal difference.
However, Tottenham will arguably face the toughest examination of their Europa League credentials yet against Galatasaray, who are fifth in the table with seven points while leading the way in the Turkish Super Lig.
Speaking at his pre-game press conference, Postecoglou confirmed that two players who would have been optimistic of starting Thursday's match - Mikey Moore and Timo Werner - would both be unavailable for the contest.
Spurs lose two attackers ahead of Galatasaray clash
Werner - who was an unused substitute in the 4-1 Premier League win over Aston Villa at the weekend - is dealing with a groin problem, while 17-year-old Moore has come down with an illness.
"Timo Werner a little bit of a groin issue he's carrying, so he didn't travel and Mikey Moore has a bit of a virus so he was left at home, everyone else who was fit should be available," football.london quotes Postecoglou as saying.
The Tottenham boss also delivered updates on the conditions of Richarlison and Cristian Romero, both of whom had to come off against Villa with hamstring and toe problems respectively.
Postecoglou did not confirm claims that Richarlison would be absent for at least four weeks, although he did admit that the Brazil international would be out for a "while", while Romero is touch-and-go for Sunday's Premier League meeting with Ipswich Town.
"From the weekend, Richy injured his hamstring. He'll be out for a while. Romero nothing too serious, still a chance for the weekend," the Australian added.
Could Postecoglou be forced to start Son Heung-min against Galatasaray?
Werner and Moore's fresh blows - coupled with Richarlison's layoff and Wilson Odobert's setback in his recovery from a thigh problem - could leave Postecoglou facing an attacking decision that he did not want to make for Thursday's game.
Captain Son Heung-min only just came back from a thigh injury of his own in the thrashing of Aston Villa, but Postecoglou was only prepared to risk him for the first hour before bringing him off and would surely have rested him in midweek had other options been available to him.
The 32-year-old was visibly miffed to be coming off early at the weekend, but with two of Spurs' recognised left-wingers in Werner and Moore not available, he could very well reprise his role in the first XI against Galatasaray.
Son has only started one Europa League game this season - the 3-1 win over Qarabag where he picked up his original injury - although Postecoglou could opt for Brennan Johnson and Dejan Kulusevski out wide instead.
The latter reverting to a right-wing role would open up a space in midfield for James Maddison to slot into, while Lucas Bergvall and Yves Bissouma are other alternatives in the engine room.