The voicemail is the most damning link between Morgan and the phone hacking scandal.
In a 2006 article in the tabloid Daily Mail, Morgan said he was played a phone message left by the former Beatle on Mills' answering machine, described it in detail in the article.
But Morgan refused to answer almost any questions about how he was able to hear the voicemail, saying, "I'm not going to start any trail that leads to the identification of a source."
Mills has said there's no way Morgan could have obtained the message honestly.
Morgan said he "doesn't believe" he had ever listened to hacked voicemail message, although he had discussed phone hacking at length in earlier interviews. He said those interviews were based on rumor and hearsay.
When asked who had filled him in about the practice, Morgan said, "My memory's not great about this. It was a long time ago."
Before his U.S. television career, Morgan ran two British tabloids - the News of the World and the Daily Mirror.
The phone hacking scandal has led to the arrest of more than a dozen journalists. Senior executives with Rupert Murdoch's News Corp. media empire have lost their jobs, and top U.K. police officers have resigned over their failure to tackle the scandal.
Murdoch shut down the 168-year-old News of the World in July after the full hacking scandal broke.
The Associated Press contributed to this report.