The former Netherlands international has conceded that the Japanese prodigy is an unrealistic target as he looks to prepare his squad for their Eredivise title defence
The Japan international moved to the Gunners in January 2010, but has since left north London on loan, enjoying spells at both Feyenoord and Bolton Wanderers.
He was particularly impressive during his stint at De Kuip, but with his path to first-team football blocked at the Emirates Stadium, has been linked with a temporary move to the Amsterdam club.
However, De Boer does not think that his side will be able to land the 19-year-old, but insists that he has several other transfer targets in mind.
"In my opinion he is not an option any more," he told Eredivisie Live. "There are several candidates. We'll know more soon."
Ajax will enter the coming Eredivisie season as back-to-back champions. They last won three consecutive titles between 1993-94 and 1995-96.