French media outlet RMC Sport reports that the centre-back has been given the ‘green light’ to return to training.
Konate hasn’t made an appearance for the Reds this season.
He suffered a knee injury in Liverpool’s final pre-season friendly of the summer - a 3-0 loss to Strasbourg at Anfield.
The former RB Leipzig defender has been on the sidelines since.
Jurgen Klopp confirmed that he expected Konate to be back to training ‘in and around’ the international break.
And if that is the case, Konate will be back for a crucial period.
The 23-year-old joined Liverpool in June 2021 and made 29 appearances in his maiden campaign.
Konate’s role in Klopp’s side grew with importance as the season wore on.
He started several important games, culminating in the 1-0 loss to Real Madrid in the Champions League final in Paris.
Meanwhile, Jordan Henderson will be back in contention to feature for the Reds against Brighton.
The Liverpool skipper has missed the past three games with a hamstring issue he sustained in the 2-1 defeat of Newcastle United in August.
However, Henderson was a late call-up to the England squad to replace the injured Kalvin Phillips.
The 32-year-old made his return to action as a substitute in the Three Lions’ 3-3 draw against Germany on Monday evening.
Before the World Cup starts in November, Liverpool have a hectic fixture list.
In total, they have 13 matches in a 42-day period to fulfil - starting against Brighton.
Liverpool endured a stuttering start to the 2022-23 campaign.
They’ve picked up a total of nine points from a possible 18 in their opening six Premier League games.
And in the Champions League, the Reds suffered a sobering 4-1 loss to Napoli before securing a late 2-1 victory over Ajax in their final game ahead of the international break.