Sir Paul McCartney's ex-wife has claimed she was hacked in 2001, when Morgan was the editor of the Daily Mirror tabloid, a publication owned by Britain's Trinity Mirror group.
In a BBC interview on Wednesday (03Aug11), Mills alleged a senior journalist at Trinity Mirror called her in 2001 and relayed a message verbatim that the Beatle had left on her voicemail.
Morgan later wrote in a 2006 column about an unspecified person playing him a "heartbreaking" phone message McCartney had left Mills after a fight, detailing how the star sang his hit We Can Work It Out to her.
The former glamour model is adamant that hacking is the only way Morgan could have heard the tape - but the journalist-turned-TV personality insists her claims are "unsubstantiated".
In a statement, Morgan says, "Heather Mills has made unsubstantiated claims about a conversation she may or may not have had with a senior executive from a Trinity Mirror newspaper in 2001. The BBC has confirmed to me that this executive was not employed by the Daily Mirror.
"I have no knowledge of any conversation any executive from other newspapers at Trinity Mirror may or may not have had with Heather Mills... No doubt everyone will take this and other instances of somewhat extravagant claims by Ms Mills into account in assessing what credibility and platform her assertions are given."
Morgan has vehemently denied taking part in Britain's phone-hacking scandal, which saw media mogul Rupert Murdoch shut down his News of the World tabloid last month (Jul11) amid allegations a private investigator working for the newspaper had illegally accessed voicemail messages belonging to celebrities, royals and crime victims.