The Japan winger spent part of last season on-loan at Bolton Wanderers.
"I think I've made big strides. Once you come to a big club, you can't walk into the team - I have to work hard every day so that I can play well in the future," Miyaichi told arsenal.com.
"Even so during training, being able to practise alongside superstars can only be a good thing. It's important to try to get noticed. All I can do is believe in myself and work hard. Otherwise it's up to the boss so I'll just do what I can."