The former Crystal Palace midfielder made the switch in August and scored twice in the 9-2 Champions League thumping of Dinamo Zagreb.
Kompany said: "I think he is playing an important role, which is not easy when you arrive in the Bundesliga and at a club like Bayern.
"He will take further steps. From my point of view, this is very positive, but I am also keeping an eye on him because I know it is important that he continues to do what he is doing if we want to enjoy good moments."
Olise was signed for €60m by the Bavarian giants in July, but only joined his new club after the Olympic Games, where he won the silver medal with France.
"For me it wasn't so bad that he went to the Olympic tournament because he arrived in great shape at Bayern Munich," added Kompany.'