The two bandmates are disagreeing over various details of Viva Forever, according to the New York Post.
Jennifer Saunders confirmed in 2010 that she would write the musical, containing several of the girl group's biggest hits.
"Mel B and Mel C just cannot agree on anything. It is driving Jennifer crazy," an insider said.
Emma Bunton, Victoria Beckham, Geri Halliwell, Mel C and Mel B are involved in the project, but will not appear in it.
When originally announced, it was hoped that the musical would open in London's West End in 2012.
Mel C recently denied reports that the Spice Girls will reunite for a performance at The Queen's Diamond Jubilee concert.
Mel B announced a new record deal with EMI Music Australia at the weekend (April 1).
> Jennifer Ellison: 'I want to be in Spice Girls musical'
Watch the Spice Girls in the video for 'Too Much' below: