Coyle is keen to tempt Miyaichi back for another year after holding talks with the Gunners.
"We'd love to have him back - he's an exciting young player and that's what we want for next year," Coyle told the Bolton News.
"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.
"Ryo certainly loved his time at the club. If we could get him back with us again, then that would be great."