The Prestige star fell in love with the tale of Beth Raymer, an exotic dancer who became a professional sports gambler, and met Frears to discuss the role - but he rejected her because she wasn't American.
Hall, however, refused to give up - and pestered the auteur for another audition when they were both in New York.
She tells Britain's Telegraph Magazine, ""When I went to meet Stephen, he said..., 'Well, it's very nice to meet you - but you're everything that I'm not looking for, for this role, and I will never cast you.'
""Literally, for six months he wouldn't let me read. He kept saying, 'Americans only...'""
But Hall won him over by dressing like a hooker when Frears finally agreed to see her again: ""I did all the things that I've never really done before; I wore the tightest jeans I could find and stuffed my bra with socks and curled my hair. Stephen was even worse than before. He said, 'So here I am against my will. I know you're wrong for this, so let's get it over with.'""
But, despite his reservations, Frears was wowed by Hall's audition - and quickly admitted he was wrong.
The director adds, ""She was absolutely tremendous. She was so convincing and outrageous and extraordinary. So I lost and I won.""