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According to The Sun, the X Factor boss is said to want Zac Efron in the lead role of Tony Manero and is interested in working with Timbaland on the film's soundtrack.
Manero was originally played by John Travolta in Robert Stigwood's 1977 movie, while the score featured a number of songs by the Bee Gees.
A source said: "Simon has been looking into buying the rights for years and opened discussions with Robert about the remake.
"The charm offensive has been in full swing and they made a breakthrough over the last couple of weeks."
They added: "Robert was keen to get some assurances the original wouldn't be completely butchered before he agreed to the deal.
"Simon has been drawing up a list of people he wants to get involved. When that meets Robert's expectations, the contracts will be signed."
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