Mark Burnett, the reality show impresario, has faced mounting demands in recent days to release old video from his series “The Apprentice,” on speculation that Donald J. Trump was captured on camera making vulgar remarks during his 11 years as the show’s host.

On Monday, Mr. Burnett broke his silence and issued a statement with a basic message: Don’t look at me.

“Despite reports to the contrary, Mark Burnett does not have the ability nor the right to release footage or other material from ‘The Apprentice,’” read a statement issued by Mr. Burnett’s public relations team and attributed to Mr. Burnett and Metro-Goldwyn-Mayer, the entertainment conglomerate that acquired a majority of his production company in 2014.

The statement did not elaborate on the reasons Mr. Burnett could not distribute the video, beyond a general description of “various contractual and legal requirements” that “restrict M.G.M.’s ability to release such material.”