The former Crystal Palace winger was a huge target for the Blues this summer.
However, Olise chose Bayern Munich and the club have not signed another winger.
Speaking with reporters, Madueke said: “Of course, I believe in my ability. We've got a great team full of great players. Players who can play in different positions. It's always good to have a team like that. I try to do my best and see what happens.
“It's competition. Competition happens at top clubs all the time. It's just one of those. It’s not anything different or peculiar. It is what it is. I feel good. New manager. New tactical ideas. It will take a little time to fully get that over to the boys but from what I've seen so far, it's promising. It's a different style of play but one I feel we're well suited to.
“It's about staying high and waiting for that killer pass when you can go and do real damage. It's about being patient and waiting for the opportunity to run and do my stuff. That's the discipline that the manager wants and if the manager wants that, then I'll do it. Simple.”