Conte was linked with the Real job when Julen Lopetegui was sacked earlier this season, but push back from the players saw the Italian pull out of talks for the post.
But Bonucci said, "With the players that Real Madrid currently has, Conte would be perfect for this job ... but it should only start in June.
"His strength you see is only if he starts working from scratch. He pushes you to give 110% of yourself.
"But it can be complicated when he takes a team in the middle of a season."