He made an immediate impact on his debut for the Bluebirds, helping his new side to a win against Norwich City, and Solskjaer insists that he sees similarities between Zaha and the Real Madrid forward.
"He is one of the best I have seen with the ball. He has quick feet and is brave like Cristiano and wants to go forward," Solskjaer is quoted as saying by The Mirror.
"But he has got to make a decision about how good does he want to be and how much does he love this game. He can grow up to become a proper player like Ronaldo if he wants.
"I have never seen anyone work as hard as Ronaldo. Before training, after training, he was an exceptionally dedicated man and proved to everyone what dedication gets you."
Zaha joined United from Crystal Palace for £15m last January.