The Argentine defender had to come off in last weekend's 4-1 thumping of Aston Villa with a toe injury, which rendered him unavailable for the Europa League loss to Galatasaray on Thursday.
Postecoglou said before that 3-2 defeat that Romero had "a chance" of being fit for Sunday, though, and the same goes for Timo Werner (groin), Djed Spence (groin) and Mikey Moore (illness).
However, Richarlison, Wilson Odobert and Micky van de Ven are guaranteed absentees due to their thigh issues; the latter's absence means that Romero will partner Radu Dragusin if he is able to play.
Guglielmo Vicario will no doubt return in goal for Fraser Forster too, as Destiny Udogie and Pedro Porro bomb down the flanks; the latter has had more shots than any other Premier League defender this season (19).
Postecoglou's biggest midfield dilemma comes in the shape of James Maddison, who scored a beautiful free kick as a late substitute against Villa, but he has no real reason to alter the trio of Pape Sarr, Rodrigo Bentancur and Dejan Kulusevski.
Son Heung-min's comeback appearance against Villa lasted just under an hour before he was taken off at half time in the Galatasaray loss, but that was seemingly a precautionary measure from Postecoglou to ensure that his captain can take his usual place with Dominic Solanke and Brennan Johnson this weekend.
Tottenham Hotspur possible starting lineup:
Vicario; Porro, Romero, Dragusin, Udogie; Kulusevski, Bentancur, Sarr; Johnson, Solanke, Son