According to The Athletic, the left-back will again be absent for the Reds.
As a result, he was sidelined for the 2-1 victory over Ajax before the international break - and had to pull out of Scotland duty.
Klopp previously admitted that Robertson would not be available until the campaign recommenced.
But as Liverpool prepare for their first Premier League game in almost a month - with fixtures against Wolves and Chelsea postponed following the death of Queen Elizabeth II - Robertson will not feature against Brighton at Anfield.
Instead, Kostas Tsimikas will continue to deputise on the left-hand side of defence.