The film is currently in pre-production, with Paul McGuigan (Lucky Number Slevin) signing on last month to helm the revisionist, science-fiction version of the Gothic classic.
Radcliffe is believed to be interested in playing the role of Hunchback, who assists Henry Frankenstein in the creation of his monster, according to The Wrap.
The new version of the film places this character, named Fitz in the book, in the lead role. He is reported to wear old clown's clothing, and has been described by sources in production as "pathologically dirty".
The film-makers are currently hard at work finalising the script, which is being written by Chronicle scribe Max Landis.
Landis recently discussed the challenges of re-interpreting the book, and gave a hint as to what to expect from the finished film.
"I began to pick apart our knowledge of Frankenstein and discovered that the public's idea of this myth comes from a million different places," he said.
"I became committed to re-contextualising it all so it all worked in one story. By the end of the day, it's a period piece and yes, it's from [Hunchback's] perspective, but man it's cool. It's the best thing I've written."