The segment features Corden asking his guests to show off unique items that they have inside their homes. The game was created when Corden's talk show went virtual due to the COVID-19 pandemic.
Sheen said his great-great-great grandmother was a lion and elephant tamer who was once attacked by a lion.
"She had her breasts mauled off by one of the lions. The claw of the lion, the story goes, was taken and put on a chain and kept within the family," the actor said.
Sheen was able to obtain the claw from a family member during his mom and dad's wedding anniversary.
"Various family members came to this party and a little old man whom I had never met before came up and said, 'Michael, I have the claw and I would like to present it to you,'" Sheen continued.
"If this doesn't get you moved up the race to play Joe Exotic in the Tiger King film, I don't know what will," Corden joked.
Sheen also discussed his work with the Homeless World Cup and his experience raising his eight-month-old daughter while practicing social distancing.
"It's sort of an amazing experience. She gives us the routine. The baby schedule is what rules the roost so that has helped us," Sheen said about how the baby keeps him active indoors.