The 19-year-old made his return to match action after a long injury stint by scoring twice in Friday's U23 friendly win over h Northwestern University.
Asked if Brewster would play against Chelsea U23s this weekend, Klopp replied: "I'm not sure.
"He got a knock with the goalkeeper - bounced in the goalie, a little bruise at the hip. We have to see. But it was good.
"We watched it here [at Melwood] in our office and it was good to see.
"I said it before, but it's nice having him in training. This week he didn't train after the game because he had the bruise, so I don't know if he can play at the weekend.
"It's good to have him back. [It was] his birthday this week, 19 years old - crazy.
"There's so much to come and only get him fit, keep him fit and then the door is wide open for him."