US star Hathaway (30) recently won a Golden Globe and is up for a best supporting actress Oscar for her performance as Fantine in Tom Hooper's Les Miserables.
She had been set to star opposite Chris Hemsworth in Steven Spielberg's sci-fi adaptation Robopocalypse, which has been pushed back.
Elizabeth Taylor and Richard Burton starred in a film version of The Taming Of The Shrew in 1967.
Anne Hathaway was the name of William Shakespeare's wife. The couple married in 1582.
Screenwriter Abi Morgan, whose credits include The Iron Lady, Shame and BBC drama The Hour, is in talks to adapt the work for film, according to reports.
No director appears to be attached to the new version.