The project is based on Nelson Johnson's book of the same name and will chart the rise of organised crime in Atlantic City during the early 20th century.
Speaking to DS, the actor said he has "high hopes" for the project.
"I've had so much research to read. I've got photos and newspaper clippings and I've been gathering all that information.
"They're putting a lot of money into it, I'm very excited."
When asked if he thought the pilot would be picked up for a full series, Graham said: "That's the intention, but we've just done a pilot. It's by the same people that made The Sopranos."
Graham, who stars alongside Steve Buscemi, Michael Pitt and Michael Shannon in the pilot, added that he wasn't keen to relocate to the US.
"I quite like where I live in Leicestershire," he admitted. "But if I have to, I'll go out there for a few months - for five months or so."