Edu has turned down an approach from Arsenal.
Globoesporte says Arsenal are looking to bring in a new technical director, which is one of the factors behind the uncertainty surrounding Sven Mislintat's future.
Mislintat believed he would get the job if it became available but Arsenal were set to overlook their head of recruitment.
Edu, who was part of Arsenal's Invincibles' squad, was lined up by the Gunners board but reports in Brazil suggest the 40-year-old has said no.
The former midfielder was offered the chance to rejoin the club but wants to stay on with the Brazil national team.