Miyaichi, who has been included on the Gunners' pre-season tour to Asia, has been tipped to be loaned out again by Arsene Wenger in order to gain more experience.
The Japanese youngster spent the second half of last season on loan at Bolton Wanderers and has previous experience of Dutch football after a stint at Feyenoord in 2011.
However, a return to the Eredivisie with Ajax appears to be unlikely after De Boer confirmed he is no longer considering a move for the 19-year-old.
"In my opinion, he is not an option anymore," De Boer told Eredivisie Live.
"There are several candidates. We'll know more soon."
Miyaichi joined Arsenal in early 2011, but has been restricted to just two substitute appearances in the Carling Cup during his time at the Emirates Stadium.
Bolton manager Owen Coyle had previously expressed an interest in re-signing Miyaichi on loan, but a decision is unlikely to be made until after the player returns from Arsenal's trip to the Far East.