According to Cadena COPE, an agreement is already in place with the Argentine, who spent six years at Mestalla as a player between 1999 and 2005.
Emery's departure has not yet been confirmed and even though the 40-year-old coach has qualified Valencia for next season's Champions League, he has come in for stern criticism for Los Che's inconsistent form this season, particularly in the wake of their Europa League semi-final exit at the hands of Liga rivals Atletico Madrid.
Consequently, he is now considering his future and admitted after Saturday night's 1-0 victory over Villarreal that Russian outfit Spartak Moscow have made an approach.
"It's one of the options I have," Emery is quoted as saying by AS.
Pellegrino, meanwhile, served as an assistant to Rafa Benitez at both Liverpool and Inter but has never before held the position of head coach at a club.
However, Cadena claims that the former defender's return to Mestalla is effectively a done deal.