Sarr - a staple of the Tottenham engine room this season alongside Yves Bissouma - has not been seen since returning from the international break with an unspecified injury, which he sustained while playing for Senegal.
The 21-year-old has been forced to sit out clashes with Aston Villa and Manchester City since domestic football resumed, while Dier was also missing from the weekend's 3-3 draw with the latter.
With Dier absent from the Etihad, full-backs Ben Davies and Emerson Royal were forced to pair up as makeshift centre-backs, with 18-year-old Alfie Dorrington providing an emergency option from the bench.
Speaking to Tottenham's media channels ahead of the London derby with West Ham, Postecoglou confirmed that Sarr and Dier would remain unavailable for the midweek encounter, but he talked up the importance of Cristian Romero's return from a three-game ban.
"Probably tomorrow might be a bit too quick for him [Sarr] but certainly should be available for Sunday. In terms of last week I guess the main one is Romero's back and available which is great," the Australian said.
"He's one of our leaders, with him and Madders [James Maddison] out it rested on Sonny's [Son Heung-min] shoulders. He's the only fit centre-back we've got at the club at the moment, with Micky and Eric Dier and Ashley Phillips all injured, it's good to get him back and get some stability.
"Eric's got a sore groin that he's been dealing with for a while, he hasn't been training so it's just trying to manage that at the moment. Everyone else got through the game well, the rest of the injuries are sort of longer-term."
Sunday's stalemate with Man City saw Richarlison make his comeback off the bench following groin surgery, and while it is still too soon for the Brazilian to start, Postecoglou has confirmed that he will be an option off the bench again.
"It was good to get him some game time, he still needs some work n training, but again he'll be available, and if we need him again towards the end of the game he'll be able to contribute," Postecoglou added.
Among Tottenham's long-term absentees are Phillips (ankle), Micky van de Ven (hamstring), Rodrigo Bentancur (ankle), Ivan Perisic (knee), Manor Solomon (knee), Ryan Sessegnon (hamstring), Alfie Whiteman (ankle) and Maddison, whose ankle injury will keep him out until the New Year.
The former Leicester City playmaker recently spoke with ex-England goalkeeper Ben Foster about his recovery, admitting that it was a "slow burner" and hinting that his recuperation period would be longer than expected.
However, speaking to reporters in his press conference, Postecoglou warned Spurs fans to take Maddison's words with a pinch of salt and insisted that he would only be listening to the advice from the medical team.
"I'm not sure about James' medical qualifications and whether we should trust his diagnosis in this situation. We should go with the medical staff and as far as I'm aware he's progressing as expected," Postecoglou added.
Tottenham are clinging onto fifth place in the Premier League table ahead of their clash with West Ham, where victory would propel them back into the top four if there is a winner in Aston Villa's showdown with Manchester City on Wednesday.