The Dutch striker was included in the squad for Thursday's UEFA Europa League victory over Torreense but was absent at the Vitality Stadium.
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The French tactician revealed that the Black Cats are carefully managing Brobbey's recovery from a hamstring injury to avoid further setbacks.
“We decided not to rush the process,” Le Bris told the club website.
“He is in a good place and has trained with the squad all week, but after a hamstring injury, it is still important to stay cautious.
“We have delayed his game time a little bit, but probably this week we will see him if everything is going right.”