The La Liga club's president Florentino Perez dismissed the Spaniard after an emergency board meeting, with their former player Zinedine Zidane poised to take over, the paper said.
Frenchman Zidane has been in charge of the Real 'B' team.
Madrid deserve credit not critics, claims Benitez
The club declined to comment. Real are third in the standings, four points behind leaders Atletico Madrid, after suffering three league defeats this season, including a 4-0 home loss to arch-rivals Barcelona.
Benitez, the former Liverpool, Chelsea, Inter Milan and Napoli manager, replaced Italian Carlo Ancelotti in June.
Benitez on brink as Real face Valencia
Real have been European champions 10 times and are the most valuable club in the world according to Forbes magazine.
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