The Oscar winner is currently starring as the legendary director's wife Alma Reville in the biopic Hitchcock, which is about the making of the controversial film Psycho.
In an interview with The Huffington Post, Mirren detailed her experience auditioning for Hitchcock's film Frenzy in the early 1970s.
"When I was a very young actress, just starting out, I was sent for an audition - or a meeting with him," Mirren recalled. "I don't think he would have auditioned me; I think he either thought you looked right or you didn't."
She continued: "I was arrogant and ignorant and, at that time, he was just not my kind of film director. I was into Federico Fellini, Pier Paolo Pasolini, Roberto Rossellini; those were the directors I loved. I was, you know, as one is when one is young, just ridiculously self-opinionated.
"So, I didn't really like him, and I know he didn't like me very much. He certainly didn't cast me. He took one look at me and went, 'Oh, good God. She's going to be a nightmare'."
Mirren went on to credit her Hitchcock co-star Sir Anthony Hopkins for creating an authentic portrayal of the legendary director.
"Quite honestly, it was weird for me, because all the hours of the day that I was on set with him, he looked like Hitch," she said. "And he was Hitch. In a weird way, Tony - in my mind - became Hitch."
The star went on to say: "That's who Tony Hopkins was. I hated seeing him take his face off. But at the end of the day he would just rip it off, because he was so sick of [the make-up].
"He would pull it off in this weird movement. I hated that, because that was the man that I loved. Do you know what I mean? Then, when the real Tony was there, it was like, 'Who's that? That's the famous actor Tony Hopkins'."
The cast of Hitchcock also includes Scarlett Johansson playing Janet Leigh and James D'Arcy as Anthony Perkins.
Hitchcock is now playing in the US and opens in the UK on February 8, 2013. Watch a trailer for the film below: