The presenter, 33, said the former Prime Minister wanted to have the pre-organised chat with him on This Morning canned because his advisors felt that the star wasn't 'qualified enough'.
Clark, who was a stand-in for Phillip Schofield on the ITV show, has detailed the experience and spoken about the pushback he receives from the public when he tries delving into subjects like politics, in his new book, Ten: The Decade That Changed My Life.
"In 2016 before the EU referendum, for example, I was due to interview Boris Johnson on This Morning.
"Then I found out he had threatened to pull out because his advisers heard that I was standing in for Phillip Schofield that day.
"Apparently they thought I wasn't 'qualified enough' to ask him questions.
"Obviously, This Morning didn't tell me this, and I'm sure it wasn't Boris who said it, it was probably someone on his team, and I did eventually interview him, but how do they know if I'm qualified or not?"
Clark does however admit that he loves when people underestimate his abilities.
He also claims that if he did pursue a career in politics he'd "wipe the floor with any frontbencher" and be able to convince the opposition to see things his way.
In the chapter titled, Rylan for PM, he shares his fantasy cabinet, with him as Prime Minister, pal Claire Richards from Steps as his right-hand woman, Victoria Beckham as Minister for Women and Equalities and Gavin and Stacey actress Joanna Page as Secretary of State for Wales.
The star also details his rise to fame after appearing on the music talent show The X Factor in 2012 as well as the impact that the breakdown of his marriage had on his physical and mental health, which included him trying to take his own life after the split from husband Dan Neal.
Ten: The Decade That Changed My Life is out now