Morgan told the BBC’s Americast podcast the prankster rang the then-president in October when he was on Air Force One.
It only emerged when Mr Trump rang the real Morgan out of the blue while on his way to vote in Florida.
Morgan and Mr Trump had fallen out after the TV host criticised Mr Trump’s handling of the pandemic.
Morgan described the prank call as “an hilarious story,” adding that “somebody had called him pretending to be me the day before and got through to him on Air Force One and they had a conversation with Trump thinking he was talking to me”.
Morgan, 55, is a long-time acquaintance of Mr Trump, 74, and in 2008 won a series of Celebrity Apprentice, a show hosted by the billionaire businessman.
They had been friendly during Mr Trump’s time in the White House before their fallout last year.
Morgan said Mr Trump was a “useless leader” because of his “character flaws – the chronic narcissism, the desire to make everything about himself”.