Morgan currently presents a talk show, Uncensored, on the newly launched channel TalkTV.
While his debut episode – which featured an interview with Donald Trump – was reported to have significantly outperformed rival news channels, TalkTV, and Morgan’s programme, has suffered a subsequent drop in ratings.
Earlier this week, Morgan wrote on Twitter: ““UPDATE: [we] beat Sky News and GB News in the UK ratings AGAIN last night.
“Still very early days, but the show is already gaining real traction around the world, making lots of news, and as I hoped, annoying all the right people.”
In response, McCoy, who has worked in the past for channels including Sky News, BBC News and GB News, wrote: “Please show the figures. #Facts.”
Morgan then replied: “Show me yours. Oh wait…”
“Retirement, Piers,” Simon shot back. “Try it.”
“What, and be as bitter as you?” Piers then wrote, adding: “No thanks.”
This was followed by a tweet from McCoy showing that he had been “blocked” by Morgan on the social media site.
“Can’t have been. He says he’s open to debate,” he wrote, sarcastically.
Morgan has spoken recently on his series about his willingness to block people on Twitter, describing it as “an exercising of my right to free speech”.