Emery says he's pushing the midfielder to continue working towards fulfilling his potential.
"He has a huge potential. We signed him thinking not about the work he did before at Everton, but how we can exploit his potential," Emery said of Onana.
"The adaptation is very important for every player, and some can get that adaptation quickly. Some need more time.
"Especially with him, last year he had injuries. It was a good season, but not like we think he can get. This year, he is progressively getting better, but his best must come. He must get it.
"He must be so, so aggressive to improve his mentality, and we are here to help him and exploit his potential progressively.
"I think his commitment to understand how he can improve or how he can get his potential - he is aware of it, and we are in this process.
"I know he can do much better. I know he can exploit his potential, and we are here; the challenge he has is to get it."