Both players have spoken openly about their individual credentials ahead of the award, with the winner due to be announced in the coming weeks.
Cañizares believes their comments risk creating an unfavourable impression among the people who ultimately decide the award.
“The person who votes is a human being and people don't like arrogant people. Both Mbappé and Lamine, I think, have lacked humility when making assessments about the Ballon d'Or.”
He added: “And I think this doesn't benefit them because the person who votes says: ‘What are these two talking about?’”
Real Madrid striker Mbappé has emphasised his goalscoring record while Barcelona's Yamal has pointed to his wider contribution and performances.
Both players are among the leading contenders to succeed Ousmane Dembélé as the holder of the award, with Harry Kane also in contention.
The timing adds another layer of interest, with Mbappé and Yamal due to face each other in the Clásico shortly before the Ballon d'Or ceremony.
Cañizares' comments provide another perspective on the increasingly public discussion surrounding the individual prize, with both players continuing to make their case for recognition.