Son was brought back sooner than expected for the 4-1 win over West Ham United just over a week ago, with the Spurs captain scoring and playing 70 minutes against the Hammers.
A hamstring injury had kept the South Korean superstar out of representing his country in October's international break, and Son had also missed the matches against Manchester United, Ferencvaros and Brighton & Hove Albion prior to that.
However, Postecoglou made the brave decision to start Son on the return of club football, despite the player requiring a very late fitness test.
Son out of important cup tie vs. Man City
A recurrence of the injury occurred after the West Ham win though, with Son reportedly feeling soreness in his hamstring, meaning he was left out of the side that edged past AZ Alkmaar in the Europa League.
However, Son was also unable to feature in the defeat to Crystal Palace at the weekend, as Spurs lost for a second away league game in succession.
Ahead of the clash with Man City in the last 16 of the EFL Cup, manager Postecoglou has confirmed that Son will not be risked, but should be fine to play against Aston Villa at the weekend in what feels like a must-win encounter on home soil.
Speaking to the media in his pre-match press conference, Postecoglou revealed: "Sonny, no. Well he is almost fit but we will probably from our perspective aim him for the weekend. We're quite confident he will be right for the weekend."
This setback will see Son sit out a sixth game in seven for Spurs, and deny him the opportunity of facing one of his favoured opponents.
Who could deputise for the injured Son?
Despite the level of Man City, Son has always had a knack of netting against English football's dominant force.
Son has scored eight times against City in a Spurs shirt, with three of those coming in cup competitions, all across the two legs of their thrilling Champions League quarter-final in 2019.
Replacing that threat will be difficult for Postecoglou, who also confirmed that Wilson Odobert will remain on the sidelines.
"The only one missing out, which is a bit of a disappointment, is Wilson (Odobert). He's had a setback during the week and it seems like it's a serious one, so we're waiting for more information." the Spurs boss announced.
Seventeen-year-old Mikey Moore was handed his first Premier League start in the place of Son at Selhurst Park on Sunday, and could be given a chance to impress again against the English champions.
Richarlison and Timo Werner represent the other options available to Postecoglou out wide, while Dejan Kulusevski could move further forward from midfield if Spurs go slightly more cautious.