Rumsfeld is scheduled to sit down with Letterman Tuesday night, the show announced.
"We are always looking for someone without a movie to plug," "Late Show" executive producer Rob Burnett told Thursday's New York Post.
A Pentagon spokesman declined to confirm the booking, saying Rumsfeld's official schedule for next week would not be released until Friday.
Burnett told the Post the Letterman show had been trying to book Rumsfeld for several years.
"It was really a question of scheduling," Burnett said of Rumsfeld's apparent sudden change of heart. "There is no particular agenda."