Mbappe has scored seven goals in his past four matches for the Ligue 1 champion after a 2018-19 season in which he netted 39 times in all competitions for his club.
Manager Mourinho is a huge fan of the 20-year-old, already a World Cup winner and one of the brightest talents in football.
"The only player that comes to my mind and with who I can compare him is Ronaldo," Mourinho said.
"I think they [Mbappe and Ronaldo] are players with unique qualities. If you play against him, he's scary."
Mbappe netted on Friday for PSG in a 2-1 defeat at Dijon.
Ronaldo, a two-time World Cup winner with Brazil, was a prolific goalscorer for PSV, Barcelona, Inter Milan and Real Madrid in a glittering career.
In addition to reminding him of the Brazilian, Mourinho also said that he was also impressed by Mbappe's character.
He said: "I spoke with Kylian for three minutes at the ceremony of the Ballon d'Or.
"He speaks with everyone with a simplicity ... remarkable, classy."
Mbappe moved from Monaco to PSG in 2017, initially on loan. Monaco vice-president Vadim Vasyliev expects Mbappe to end up at Real Madrid, like Ronaldo.
Vasyliev told Telefoot that Mbappe said to him: "I want to become a great player here [France], Real will wait. But it will come."