The 19-year-old made two substitute appearances for Arsenal earlier this season, including an outing in the 2-1 Carling Cup win over Bolton in October.
Owen Coyle signed Miyaichi in January and the Japan youth international has started five league games for the Trotters, setting up two goals.
Arsenal forward Walcott is confident the former Feyenoord midfielder will return to The Emirates a better player and he is expecting Miyaichi to feature in Arsène Wenger’s side on a regular basis next season.
“Ryo has done very well at Bolton,” Walcott told Arsenal’s website.
“It is hard for such a young kid to go there and do what he is doing, showing no fear with everything that happened at Tottenham [with Muamba]. It is hard and it has probably hit him definitely.
“He will be a better person for it, a better player and I can see him coming back here next year and playing a lot more regularly.
“The way he is playing, there are full backs out there now who are thinking, ‘I don’t want to play against him this week’.”
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