Bandmates Chisholm, Emma Bunton, Melanie Brown and Geri Halliwell are allegedly keen to get back together and launch a new assault on the pop charts with fresh music and an accompanying tour without Beckham, who has established herself as a top fashion designer since the group split in 2000.
The Wannabe hitmakers are rumoured to be considering replacing Posh Spice with a new member, and Sugababes singer Heidi Range has already been linked to the job thanks to her close friendship with Bunton.
A source tells DailyMail.co.uk, "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."
A representative for Beckham appeared to fuel the tabloid claims by saying: "Victoria respects all of the girls and will always support them all personally and professionally."
However, Sporty Spice Chisholm has moved swiftly to dismiss the allegations, insisting the reports are unfounded - although she stopped short of addressing talk of new Spice Girls music.
Taking to her Twitter.com page on Sunday (16Dec12), she writes, "It seems there has been some Spice related nonsense written today. None of the Spice Girls would ever or could ever be replaced #justsayin."
The Spice Girls staged a casual reunion at the London premiere of their new West End musical Viva Forever! last Tuesday (11Dec12), but Beckham did not join her old pals for pictures and opted to pose for the cameras with her soccer star husband David and their children instead.
The band last came together to perform at the Closing Ceremony of the 2012 London Olympics over the summer (12).