Mourinho is widely expected to take over from Manuel Pellegrini at the Bernebeu once Saturday's Champions League final is out of the way.
However, Liverpool boss Benitez - who has been repeatedly linked with the Real post himself in the past - is not sure about the seemingly impending appointment.
"I know Mourinho has dreamed a lot of coaching Real Madrid but I do not know if he is the right person to train Madrid," said the Spaniard.
"Pellegrini has done a great job and deserves great respect because he's still coach and it's not pleasant to hear talk about who's going to replace you."
Mourinho himself is keen on the job.
"My only options are Madrid or Inter," he told Marca.
"To get me to leave this club after two years of incredible work, only Real Madrid could achieve that. If I go, I will move with a clear conscience having changed the club.
"All I say is that if you are a coach or a great player to not play in a club like Madrid, leaves a hole in your career.
"I want to coach Real 100 per cent. If it is next year or later, I can't say."