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The actor walked out of Comic Relief Does The Apprentice in 2007 after coming under attack from Morgan.
Everett told the Evening Standard: "Piers Morgan has done an interesting thing in the last year or so. He obviously took some good advice, because being too nasty isn't right for a TV career.
"He's obviously after the Parky lot. Piers used to be nasty and tear people to shreds but now he does these interviews where he has taken that amazing thing of [Michael] Parkinson's, which was to say nothing funny or interesting and be loved for it."
He added: "I don't know if Piers can pull it off, though, because underneath that pink, soft exterior there is still the iron claw. I have been terrified of him since Celebrity I Am an Apprentice, or whatever it was called.
"It was like going back to the first day at public school. I could smell the disinfectant and the oncoming crowd of bullies. Whenever I see him, I just want to run a mile."
