The 20-year-old Japan international joined the Gunners in January 2011 after a successful trial at the Emirates Stadium the previous summer.
However, the winger has yet to make a senior appearance for the London club, enjoying loan spells at Feyenoord, Bolton and Wigan.
His spell at the Latics last season was brought to a premature end when he sustained ankle ligament damage during an FA Cup tie at Everton in March.
He is expected to be fit in time for the start of the season and Koeman confirmed he is keen on bringing the player back to the De Kuip Stadium.
"It's right we are also working on Ryo Miyaichi, but at the moment it's not clear what the situation is," he told NuSport.
"After that, we can make a step. It's not that far yet."