According to the Daily Mail, the band may launch a talent show to find a replacement for Posh Spice, while Sugababe Heidi Range has also been suggested as a possible stand-in.
A source told the newspaper: "The girls are going it alone without Victoria. They are keen to get back together and were trying to work out if they could do it as a four-piece. I think they know this is the last chance for them to get the band going again.
"But the Spice Girls as a foursome is not going to get them another record deal or sell out big venues. They need an extra cherry on the cake. And the cherry on the cake would be if they replaced Victoria.
"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."
The publication has speculated that the remaining four members may hold auditions for a new member in a reality TV show.
The spokespeople for Melanie Chisholm, Melanie Brown, Geri Halliwell and Emma Bunton have not confirmed or denied rumours of a reunion or TV talent show.
Beckham's publicist said: "Victoria respects all of the girls and will always support them all personally and professionally."
Rumours of Beckham's lack of enthusiasm for a reunion follow the first night of the Spice Girls musical Viva Forever!, where the fashion designer reportedly arrived late, missed a photoshoot and kept her distance from the other girls then left the after-party earlier than the rest of the band.