"I feel a little guilty for asking this, but there is a story out there [today] that you guys are expecting," Guthrie asked the 50-year-old actor.
"Expecting what?" the Oscar nominee replied, seeming completely oblivious to the swirling story.
"A baby!" Guthrie explained.
"A child? Good god, what do you think I am, a savage?" he added, with a smile. "No, no truth to that."
Depp continued that the couple's wedding is "not a shotgun affair."
Depp, who met Heard on the set of their 2012 film The Rum Diary, stayed mum about his upcoming nuptials but couldn't help but gush about his future wife.
"She's a wonderful girl," Depp said about the 27-year-old, who next stars in London Fields. "She's sharp as a tack. A southern belle and sweet as can be, and very good for me."
(E! and Today are both part of the NBCUniversal family.)