The position of current coach Santi Denia is under threat after Spain's quarterfinal elimination by England over the weekend.
It is now expected that Denia will leave the job, and Raul is one of the potential candidates to take over.
Raul recently left Castilla at the end of last season, where he was replaced by Alvaro Arbeloa.
His experience working with young talent at Real Madrid's La Fabrica system has made him a serious contender for the Spain U21 job, according to the RFEF.
