Madonna is co-writing, producing and directing W.E., a biopic about the life of Wallis Simpson, and Farmiga has previously been linked to the lead role.
"She approached me," Farmiga told E! News. "We sat for a cup of tea and again for a cup of tea. Hopefully it will all come together."
She continued: "I'm actually not familiar with her work, and I told her this flat-out. She sent a couple of films and I still haven't seen them. But no matter. I don't really go by that. I go by other things. I go by scripts. I go with what I think I can do with a character and if I feel a kinetic energy with someone and I feel we can uplift and challenge each other."
Farmiga also insisted that she isn't worried that Madonna's directorial debut Filth And Wisdom was panned by critics.
"I certainly have things I wouldn't want people to see," she explained.
> Madonna signs Cornish for 'W.E.' role