The group was tipped to be looking for a star who has been in another successful band as their fifth member, the source said.
Though there would be interest in a television series about their search, they were more keen to pull in someone with industry experience.
"And that leads to the next question: who do they replace her with? At the moment it's all being done in a very cloak-and-dagger way and not through official channels."
When asked to comment on the speculation, a spokesperson for Beckham would only say: "Victoria respects all of the girls and will always support them all personally and professionally."
Among those rumoured to be in the running to replace her is former Sugababes star Heidi Range, 29, who is already close friends with Bunton.
Last week Beckham and her family posed separately from the group and hid away during the Viva Forever! after-party.
The 38-year-old fashion designer arrived at the marquee on the banks of London's River Thames on Tuesday evening with her husband David Beckham, 37, and sons Brooklyn, 13, Romeo, 10, and seven-year-old Cruz after the opening of the Spice Girls musical at Piccadilly Theatre.
Instead of joining the rest of her bandmates on the dancefloor, they sat quietly in the corner.
- Bang! Showbiz