Cooper tells the magazine that his first reaction was to think that his mom would be "so happy" and that he's "decent-looking."
The 36-year-old actor dated Renee Zellweger for two years and has recently been linked to Jennifer Lopez.
However, Cooper says he's single.
Other actors who have received the "sexiest" label include George Clooney, Brad Pitt, Johnny Depp, Hugh Jackman and Ryan Reynolds.
People's "Sexiest Men" issue is on newsstands Friday.