The 19-year-old Japanese winger enjoyed a productive spell in the Dutch Eredivisie with Feyenoord last season, and is tipped for a big future.
After returning to the Emirates Stadium in the summer, Miyaichi had been expected to make his first-team breakthrough in Arsene Wenger's side this year, but has struggled for regular playing time.
The Gunners have a number of promising midfield stars waiting for their chance at Arsenal, including Emmanuel Frimpong, who recently completed a loan move to Wolves for the rest of the season, and summer signing Alex Oxlade-Chamberlain who has waited patiently on the fringes.
Wenger is now considering letting Miyaichi leave in January in a bid to continue his development despite having worked tirelessly to grant the Asian star a work permit this season.
"Nothing has been decided," said Wenger. "We will have a look at the whole squad.
"He needs to play now and I will sit down with him and see what we will do. He has been injured for a while now and we will see in January."
A return to Feyenoord is another viable option for Miyaichi, but it is believed that Arsenal would prefer him to remain in England to acclimatise to the rigours of the Barclays Premier League.