The forward sustained a hamstring injury during a Spurs' Europa League match against Qarabag on September 26th in London. Spurs are on the back of five straight wins across all competitions.
Tottenham defender Destiny Udogie, who missed Thursday's 2-1 win at Ferencvaros in the Europa League due to a right quad injury he sustained during their 3-0 win at Manchester United last weekend, is expected to return.
"Sonny is unlikely, he's pushing hard, but the turnaround might be too quick for him to be available at this stage," Postecoglou told reporters on Friday.
"First thing's first, we're all good after last night (in Hungary), tired, but physically no issues of the guys who stayed back. Destiny we think will be okay. We train today and tomorrow, so he has to get through that."
The Korea Football Association said on Friday Son has been dropped from the 26-man squad for the third round of World Cup qualifiers to protect the player's health. South Korea play Jordan on October 10th and Iraq on October 15th.
Tottenham's new striker Dominic Solanke was named in England interim manager Lee Carsley's squad for next week's Nations League games against Greece and Finland, seven years after gaining his only senior cap.
Asked if he was surprised by the decision, the Australian coach said: "I don't know about being surprised, with Dom he's had to work awfully hard in his career. It's important to all young players that the trajectory doesn't always go in a linear fashion.
"He was at big clubs (Liverpool, Chelsea), didn't get started before but didn't deter him, went to Bournemouth and did well. I've had him for a month, I've had zero to do with his call-up, it's all down to him."
Tottenham's previous Premier League trip to Brighton in December last year ended in a 4-2 defeat. Brighton lost 4-2 to Chelsea in their last match and have picked up nine points from six games.