The film will be a big-screen adaptation of "Furious Love," a book about the couple's stormy relationship, which began when they met on the set of "Cleopatra" in 1962, Britain's The Daily Telegraph said.
Scorsese's film credits include "Shutter Island," "The Departed," "Gangs of New York," "Goodfellas," "Taxi Driver," "Mean Streets" and "Raging Bull."
Taylor died this year at the age of 79. Burton died in 1984 at the age of 58.
The couple married in in 1964, divorced in 1974, remarried in 1975, then divorced again in 1976.
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