The manager is one of Marlow's assigned "devils" in the company. As he overhears the manager speaking with his brother, he realizes that the manager in now way has the well-being of Kurtz in mind. He is afraid for his own job and is jealous of his successes. Unfortunately his rogue status has given him a reason to interfere with the workings of the Inner Station.
The manager knows that Kurtz is ill, close to death, and he has been depriving him of shipments of necessary medication. At this point, he needs Marlow to do his dirty work: to find Kurtz and to get him out of the way. The manager is banking on the fact that once Kurtz is located, he can be removed from his post for "medical" reasons and not cause the company any embarrassment. In fact, his dream comes true when Kurtz dies en route.
The manager needs someone to find and remove Kurtz from his station before he reflects poorly on the direction and operation of his (the manager's) post.