The Frenchman will replace Santiago Solari, who was in charge for less than five months, BBC Sport reported.
Former Real midfielder Zidane, 46, left in May after leading the club to a third straight Champions League trophy.
Real is currently third in La Liga, 12 points behind leader Barcelona.
Solari is set to be sacked after a 4-1 win over Real Valladolid on Sunday – which followed a shock Champions League exit to Ajax.
That 4-1 home defeat and 5-3 aggregate loss to the Dutch side was the final straw for Real president Florentino Perez.
The defeat by Ajax followed two consecutive defeats by Barcelona in El Clasico – a 1-0 loss in La Liga and a 3-0 thrashing in the Copa del Rey.
Zidane stepped down following the Champions League final victory over Liverpool, and Julen Lopetegui was hired as his successor just before the World Cup where he had been due to lead Spain, which promptly sacked him.
Four and a half months later it was Real's turn to fire him.
Reserve-team boss Solari came in as caretaker before being given a contract to 2021 on November 13.
Despite returning just nine months after he left the club, Zidane faces a rebuilding job at Real Madrid after its Champions League dynasty came to a remarkable, humiliating end last week.
Real has not adequately replaced Cristiano Ronaldo, who left for Juventus in the summer, with Karim Benzema the only Real player to reach double figures in La Liga (13). He has scored 22 goals in all competitions, with Gareth Bale on 13 and Sergio Ramos on 11.
None of those players have certain futures at Real, with captain Ramos, who has been at Real for 14 years, reportedly falling out with president Perez. Wales forward Bale is expected to leave because of a fractious relationship with the club's fans – who have booed him recently – and players.
Other stalwarts of recent glory like Marcelo and Toni Kroos have struggled too.