Alderete missed the Chelsea game with concussion and Adingra was also absent because of a minor hamstring complaint.
But the winger has recovered quickly and will be back in the squad for Monday’s night’s game, and Alderete has also now returned to training.
The centre-half will be closely assessed over the weekend before a final decision is made, but Le Bris expects the Paraguayan to return to the squad.
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“He’s getting better, trained normally with the squad this morning, he’s on the way,” Le Bris said of Alderete.
“He is still a doubt for Everton because he is in the concussion protocols, but we hope that he will be out of them tomorrow [on Saturday].
“Simon Adingra missed the Chelsea game because he had a small hamstring injury, but it was not serious. He missed one weekend but he is available.”
Dan Neil has also been recovering from a minor concussion suffered in training, but is expected to be available to be part of the squad against Everton.
None of Sunderland’s longer-term absentees are ready to return, with the likes of Romaine Mundle, Dennis Cirkin, Aji Alese and Leo Hjelde all working their way back to fitness.