Speaking after Miyaichi played 45 minutes of Arsenal's 2-1 victory over Urawa Red Diamonds on Friday, the Frenchman said it is now time for him to progress at the Emirates.
Wenger said: "He did well, he's sharp and he's in the team. I like him.
"I believe that he is in a position now where he needs to play to have a good chance to play at the top level.
"At the moment he stays in the squad. If we buy more players I will reassess the situation. At the moment though, he will definitely stay with us."
Wenger signed Miyaichi in January 2011 and immediately loaned him to Feyenoord.
Miyaichi was later loaned to Bolton in January 2012 and to Wigan in August 2012.
He returned to action in March after being sidelined for four months with a right foot injury.