According to showbusiness correspondent Baz Bamigboye the Oscar winning actress "has been asked to consider" playing Sylvia Llewelyn Davies whose four sons inspired J.M. Barrie (Julian Ovenden) to write Peter Pan.
The 2004 film starred Johnny Depp as Barrie and Kate Winslet as Sylvia.
Rob Ashford is to direct the show which features music and lyrics by Scott Frankel and Michael Korie and a book by Allan Knee who also wrote the film.
Bamigboye admits that Paltrow's involvement is a long shot but argues "it’s not totally out of the question when you consider the enormous pleasure she derived from singing several numbers when she guest-starred as relief teacher Holly Holiday on Glee".