The Italian says Zhirkov's performance upon joining the club is now legend.
Ancelotti explained in his autobiography: "Zhirkov is a midfielder with a host of talents and just one shortcoming: he can't sing.
"If you want to join this team it's not enough to sign a contract. There's another hurdle, and it's the toughest, where pity isn't a word, where mercy isn't shown.
"A player has to make it through karaoke night - a sacred ritual. It was in Los Angeles on our summer tour. The team had been ribbing him for days.
"He stood on a stool and began. I've never heard anything that bad. It was a disaster, he didn't hit one note. Pieces of bread were flying within seconds, followed by pieces of whole fruit. He went on singing like a drowning cat, like a stuck pig, for two solid minutes.
"The entire roster of players refused to take pity on him, refused to interrupt that bloodcurdling cacophony. Petr Cech wanted to put on his helmet to protect his ears. Zhirkov still hasn't fully recovered from the trauma."