Brewster was one of the most impressive performers during the early stages of the summer, netting four goals in the Reds' first three games.
Klopp said: “He's close but for him this was his first first-team pre-season. After a long injury, long, intense.
“It started really well then pre-season knocked him down, you really feel your legs, but we are super positive about him. No pressure.
“With the talent and attitude he has, it will be fine, but when I don't know. In a lot of pre-season moments he looked really good. The future is bright."