The band’s 1967 song Let’s Spend the Night Together is set to be included in the 30 classic rock tracks that feature in Carnaby Street: The Musical.
The producers of the new show said they have gained permission from the Stones’ New York-based publishers to use the track.
However, Sir Mick Jagger and Keith Richards claim that they have not approved the use of their song.
A source close to the band told the newspaper the duo “do not want to be associated with this musical” and believe they have a ”right to stop their song being used.”
Bob Tomson, the show's director, who previously worked on the West End hits Dreamboats and Petticoat, told the Independent:
Carnaby Street: The Musical tells the story of Jude, a working class boy from Liverpool, who travels to London with his guitar aiming to fulfil his dreams of fame and fortune.
The show's soundtrack will include hits from The Kinks, The Who, The Animals and Manfred Mann.
Former EastEnders actor Sid Owen stars in the musical, which is scheduled to open at the Hackney Empire in April before going on a nationwide tour.
Formed in London in 1962, the Rolling Stones are estimated to have sold more than 200 million albums worldwide.
The band reunited for a series of gigs late last year to celebrate their 50th anniversary.
Last week the Rolling Stones scooped the awards for Best Live Band and Best Music film for Crossfire Hurricane at the NME music awards in East London.