The winger is yet to make a senior appearance for the Gunners but could be set for some more first-team action with the Dutch club, where he scored three goals in 12 games in 2011
The 20-year-old was loaned out to the Eredivisie outfit shortly after joining the Gunners in January 2011, following a successful trial at the Emirates Stadium the previous summer.
The Japan international is yet to make a senior appearance for the north London club and has also spent time at Bolton and Wigan, and Koeman has revealed discussions are underway.
"It's right we are also working on Ryo Miyaichi, but at the moment it's not clear what the situation is," Koeman told NuSport.
"After that, we can make a step. It's not that far yet."
Miyaichi’s time with the Lactics last season was brought to a premature end after just four substitute appearances as he sustained ankle ligament damage during an FA Cup tie at Everton in March.
Despite the injury, he was grateful for the opportunity to gain some Premier League experience and work under Roberto Martinez, who has since taken the reins at Everton.
"It was disappointing for me but I'm so appreciative to the Wigan supporters, the Wigan manager and the Wigan players," Miyaichi told the club’s official website in April. "It was a very good experience.
"Being there helped me to grow up. As a person, I'm growing up every day."
He is expected to be fit in time for the start of the season, when he could be linking back up with Koeman at the De Kuip Stadium.