Santiago Solari is Real Madrid's preferred candidate to replace Julen Lopetegui, according to Sky in Italy.
Former Chelsea head coach Antonio Conte is also in the frame to replace Lopetegui, who took training on Monday morning before he was sacked later in the day. But it is thought Real have a preference for an "internal" candidate.
Real officials met on Monday to discuss the managerial situation, less than 24 hours after Lopetegui's side suffered a 5-1 defeat to Barcelona. The loss at the Nou Camp was Real's fourth in five matches, leaving them ninth in La Liga.
Former Real player Solari currently manages the club's B team, Castilla, who are fifth in Group 1 of Segunda Division B.
Solari won the Champions League and two La Liga titles with Real after joining the club from cross-city rivals Atletico in 2000. The Argentine spent five years at the Santiago Bernabeu before leaving for Inter where he lifted three Serie A titles in three seasons at the San Siro.
Lopetegui's predecessor Zinedine Zidane also managed Castilla before he became Real manager in January 2016 when the club sacked Rafael Benitez.