The 19-year-old, who returned to Japan on Tuesday for his expected full international debut against Azerbaijan on May 23, said he wanted to prove his worth to Arsene Wenger's side.
"I want to become their best player and be the sort of player who can carry them in games," Miyaichi told reporters after landing in Tokyo.
"I wanted to be on the pitch and help Bolton survive the drop so it was really disappointing. Now I have to get ready for the Olympics and World Cup qualifiers if I'm selected."
Miyaichi, who spent the season on loan to Bolton, where he made his Premier League debut, is expected to play in the World Cup qualifying warm-up against Azerbaijan in Shizuoka.
"It has been my dream to stand on the pitch representing Japan since I was small," he said. "My biggest weapon is speed and when I get the chance I'll show exactly what I have."
Inter Milan defender Yuto Nagatomo, who also arrived on Tuesday, stressed the importance of a convincing win against Azerbaijan before three key 2014 qualifiers in June.
"This is crunch time for Japan," he said. "Beating Azerbaijan will be crucial with final round World Cup qualifying games right after. We have to win and win well."
Japan face Oman on June 3 and Jordan on June 8 in Saitama before meeting fierce regional rivals Australia away four days later.
The form of the Asian champions has dipped with two defeats in their last three matches following an unbeaten run of 16 games since Italian Alberto Zaccheroni took charge.
The return from injury of CSKA midfielder Keisuke Honda, whose goals helped Japan reach the last 16 of the 2010 World Cup, should give Zaccheroni's side a timely lift.
Never the shrinking violet, Honda swept through arrivals Hollywood-style in a beige suit and sunglasses, saying only: "I want to show people I'm back!"
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