O'Donnell, who used to host a talk-show of her own, said on her blog the incident occurred when Letterman was unexpectedly hospitalized in January 2000 for heart-bypass surgery, the New York Post reported.
The actress said she spoke to CBS head Les Moonves the day the Letterman news broke. She said she told Moonves that if he was stuck for a host, he could let her know.
She claims executive producter Rob Burnett called her two days later and accused her of trying to steal Letterman's job. She said he told her: "You are not a friend of the Letterman show."
She said the incident caused her to refuse an invitation to appear on the show last week.
"I don't know how to respond to something that never happened," Burnett said. "And the last thing I want to do is get into a fight with a powerful celebrity who has a blog read by tens of people."