Winehouse, 27, has befriended the animal while she is on a brief holiday in the Caribbean island, according to British newspaper The Sun.
The monkey is said to have followed the star around after it first came up to her last week.??
A source told the newspaper: "Amy has made friends with a monkey, it came up to her and she fed it and it's been following her around.
"She's been telling friends how much she loves it and would love to bring it back with her." ??
The Back to Black singer is said to be in Barbados working on her new album.