The Trotters manager believes that his young charge may have a more fulfilling year in the Championship than he would as a bench-warmer under Arsene Wenger
The 19-year-old had a breakout spell with Bolton after joining on loan from Arsenal, making his first 12 league appearances and even scoring an FA Cup goal.
But although the Wanderers were relegated to the Championship on the final day of the season, Coyle believes an active season in the second tier may prove more advantageous than another campaign on the bench at Arsenal.
"We'd love to have [Ryo] back," Coyle told The Bolton News. "He's an exciting young player and that's what we want for next year.
"I've had a discussion with Arsenal already and it's only early days in the summer but we'll see how that pans out."
Coyle also praised the work ethic of Miyaichi, whose appearances decreased in the late stages of the season due to injuries.
"He had such a big heart that he wanted to play his part," the manager said. "[But] we had to take him out of the firing line."
Word of Miyaichi extending his time with Bolton comes as Japan coach Alberto Zaccheroni prepares to give the youngster his first cap against Azerbaijan on Wednesday evening.
"It's likely that Miyaichi will get an appearance," the Italian tactician said at Tuesday's pre-match press conference. "The point of this match is to give our Europe-based players a chance to regain their on-the-field intuition."
An unused substitute in Japan's last match against Uzbekistan in February, Miyaichi anticipated a chance to demonstrate his abilities against international competition.
"When I'm with the national team, my job is to demonstrate my style of football to my team-mates," the player told reporters. "We need speed in front of the goal, so all I can do is try to provide that."