The Spaniard, who was an assistant under Mourinho during the Portuguese's three-year spell in charge at Los Blancos, is convinced that the former Manchester United boss would have offered as much in the hot seat as Zidane.
"Either of the two options would have been great, but you have two different profiles," Karanka told MARCA.
"It seemed that [Ole Gunnar] Solskjaer had fixed everything done badly by Mourinho at Manchester United, but now they are out of the Champions League.
"In Jose's first season at the club, he won three trophies [the Community Shield, Carabao Cup and Europa League].
"Football moves so quickly that people forget the good things somebody does and only speak about the bad things.
"Jose will return to the level that we're used to see him manage at."