Hall - whose previous movie roles include The Town, Frost/Nixon and her Golden Globe-nominated performance in Vicky Cristina Barcelona - is eyeing the female lead role opposite series star Robert Downey Jr, reports Variety.
The role is that of a scientist described as a foil for Downey Jr's character Tony Stark. The character reportedly helps to create a new nanotechnology that is ultimately sold to terrorists.
The Help star Jessica Chastain was in negotiations for the part, but had to drop out due to scheduling difficulties.
She wrote on her Facebook page: "Sorry to say that Iron Man 3 isn't going to work out. My schedule is jammed packed and I can't fit anything else in.
"The press announced my possible attachment far too soon. I know many of you wanted me to be involved, and I'm so sorry to disappoint you."
Watch Rebecca Hall talking to Digital Spy about The Awakening below: