Zidane, 48, failed to retain the La Liga title with Los Blancos as Atletico Madrid were crowned champions of Spain on a dramatic final day of the season.
Madrid also fell short of reaching the Champions League final after Chelsea dumped the Spanish club out in the semi-finals.
Los Blancos confirmed on Thursday that Zidane, who won three consecutive Champions League titles with the club, had ended his second spell in Madrid.
Madrid have identified Pochettino as one of their top targets to replace Zizou for the following season, according to reports.
However, Madrid president Florentino Perez could scupper Tottenham chairman Daniel Levy's approach to bring the 49-year-old Argentine back to England.
COPE reports that Conte is on Madrid's radar alongside Pochettino as they search for Zidane's successor.
The ex-Chelsea and Juventus manager's ambitious plans with the Italian champions were hindered amid Inter's growing financial troubles.
Former Madrid midfielder Xabi Alonso is currently the manager of Real Sociedad B and another potential target for Los Blancos.
The 39-year-old Spaniard, who spent four seasons at the Santiago Bernabeu, began his coaching career at Madrid U14s before moving to his Sociedad B role in 2019.
Alonso was linked with Bundesliga side Borussia Monchengladbach in March, but the Sociedad B manager signed a new one-year deal with the Spanish club.
According to reports in Spain, Madrid legend Raul is reportedly the leading favourite to become the new Los Blancos head coach.
The 43-year-old Spaniard enjoyed a prolific 16-year senior playing career at Los Blancos and is currently the manager of Real Madrid Castilla.
Raul hasn't been shy to hide his desire to succeed Zidane at Madrid, saying that the senior team is "my home and that's where I want to be."
Featured Image Credit: PA
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