The 45-year-old, who previously played musician Ray Charles for a movie, has been tipped to portray the controversial sportsman.
"Jamie's the best," the Daily Star quotes Tyson as saying. "He has the look."
Foxx is also quoted as saying: "I have to do that movie. I think it would be very exciting. People talk about how he became world champ, his relations with promoter Don King and what he went through."
Tyson has also revealed that he only stopped drinking alcohol and taking drugs within the last week, despite previously stating that he was clean for a longer period of time.