Kenneth Branagh in talks to star in Laurence Olivier-Marilyn Monroe film

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Michelle Williams may also feature in film depicting squabbles between the two greats during the making of a 1957 movie
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Harry's game ... Kenneth Branagh as Henry V, which led to comparisons with Olivier. Photograph: Everett Collection/Rex Features

Kenneth Branagh famously found himself touted as the natural heir to Sir Laurence Olivier after reprising the actor's classic role for his 1989 version of Shakespeare's Henry V. So it's perhaps fitting that Branagh is in talks to portray Olivier in a film that will detail the latter's squabbles with Marilyn Monroe during the 1957 production of The Prince and the Showgirl.

Production Weekly reports that Michelle Williams, who starred in Brokeback Mountain and Shutter Island, looks likely to play Norma Jean. The film, My Week With Marilyn, is based on the diaries of Colin Clark, who worked for Olivier during the period and was Monroe's chaperone in London.

Clark, son of the art historian Kenneth Clark and brother of the Conservative politician Alan Clark, originally published his memoirs in 1958 but left out stories of the clashes between his employer and the American actor, who was close to the peak of her Hollywood fame when she arrived in the UK. In 2002 the missing entries were finally made public, and now form the basis of the screenplay.

The main obstacle to Branagh's casting could be the Belfast-born actor's ongoing directing career. He is currently shooting the comic-book tale Thor for Marvel Studios, which is due in May next year. My Week With Marilyn is expected to begin production in September, which may cause scheduling difficulties.

Earlier this year it was reported that Jake Jagger, son of Mick and Jerry Hall, was in talks to play Clark, who died in 2002. That role would appear to be a large one, as the diaries also focus on Clark's own relationship with Monroe. He reports a skinny-dipping trip to the Thames and a visit to Windsor Castle, among other outings, and even claims to have enjoyed a kiss and a brief fumble beneath some blankets. At the time, Monroe was married to the playwright Arthur Miller.