The 'Drop It Like It's Hot' hitmaker – whose real name is Cordazar Calvin Broadus – used to "dream" about becoming as famous as the 'Valkyrie' actor but is convinced the tables have turned over the past few years.
He said: "When I started to star in films I used to say, 'I dream of becoming the black version of Tom Cruise.' Today I think it's the other way round, 'Tom Cruise could dream of becoming the white version of Snoop Dogg.' "
The rapper – who has appeared in several movies during his career, most recently 'Bruno' - has never lost his movie star ambition and would love to appear in a movie about the life of the late US musician Miles Davis.
He told Zeit magazine: "One day Quincy Jones said to me: When you rap it sounds like Miles Davis playing his trumpet. I became curious and wanted to know more about him. I started to listen to his records and read about him.
"For me Miles isn't a hero, but a desire and a challenge. Miles didn't care what people or critics thought about him – he just played his music and kept developing himself as a person. He just did his own thing. That's the reason why I want to play him. His brilliant story needs to be told."