The self-confessed Liverpool supporter revealed he was on the verge of a move to Goodison Park before a meeting with the soon-to-be Manchester United boss scuppered the deal
The Cardiff striker, a boyhood Liverpool fan, says he had agreed terms with the Merseyside club but opted out of a move following talks with the Scot, who will take over at Manchester United this summer.
The former Wales international spoke to the Toffees when he was on his way out of Newcastle but made a swift u-turn on the transfer after being presented with a peculiar set of rules.
In his autobiography, serialised in the The Mirror, Bellamy says: "I was told to not shake my head if given an instruction during a game and to speak directly to Moyes only if I had anything on my mind."
The 33-year-old ended up going to Celtic on loan that summer, before sealing a permanent switch to Blackburn.
"I would have signed without that second meeting, but now I couldn't," Bellamy wrote.
"I don't hold a grudge and have got a lot of time for him. My guess is someone told him I would be trouble, and he panicked."
The Welshman will come up against both Moyes and Everton next season after helping Cardiff secure promotion to the Premier League by winning the Championship.