The 35-year-old actress has been approached by Fox to star alongside Jackman in the movie, which tells the true-life story of celebrated circus owner and entertainment impresario P T Barnum, who was responsible for a number of hoaxes, reported Deadline.
Williams recently received a Tony nomination for her part in Broadway's "Blackbird" and so is ideal for the musical role.
Her most recent credits include "Manchester by the Sea", and "Certain Woman", where she starred alongside Kristen Stewart.
The contemporary musical has been in development since 2009 with Sex and the City's Jenny Bicks set to write the script and Chernin Entertainment, Laurence Mark and Hugh producing.
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