The Black Cats, who are enjoying an impressive start to life under Le Bris, currently sit seventh in the Premier League with 17 points from nine matches.
With one game in hand over most of their rivals, Sunderland could climb as high as second if they defeat Everton at the Stadium of Light on 3 November.
Sunderland come into the fixture buoyed by a dramatic 2-1 victory over Chelsea, which continued their strong early-season form.
Speaking to the Sunderland Echo, Le Bris revealed that Alderete, who has been sidelined with a concussion since the win over Wolverhampton Wanderers, is close to full fitness.
“He is improving; he trained normally with the team this morning, and he is on the right track,” Le Bris said. “He is still doubtful for the match against Everton because he is under concussion protocol. Simon Adingra missed the match against Chelsea due to a small hamstring injury, but it was not serious.
“He missed one weekend but is already available.”
The return of Alderete and Adingra will be a major boost for Sunderland, who have surprised many with their disciplined defence and attacking flair.
Adingra’s pace and creativity have been missed on the wing, while Alderete’s composure at the back has been key to the team’s solidity.
Everton, meanwhile, are struggling for form and sit 15th in the table with 11 points after back-to-back defeats to Manchester City and Tottenham Hotspur. David Moyes’s side have looked short of confidence and face a difficult test against a Sunderland team brimming with belief.
With momentum on their side and key players returning, Sunderland will fancy their chances of securing another statement win to strengthen their push for the top spots in the Premier League.
