However, a source close to the sale thought Absolute Radio would buy the radio stations, regardless of whether it could come to an agreement over keeping the brand name.
The source said: "Even if the two parties can't negotiate a deal over the Virgin name, Absolute Radio will buy the radio station anyway and it is considering calling it Jack FM.
"It owns this station in Oxfordshire and it is a big brand in the US."
Steve Parkinson, marketing director for Bauer Radio, added: "I know when other companies looked at buying Virgin, there was divided opinion over how much value the brand name added.
"Some companies felt it would increase ad revenue opportunities, whereas others felt it was associated with too many other industries.
"If Absolute Radio does take over and decide to rebrand as Jack FM, and they have the money to properly launch a new brand, it could be very interesting for the radio industry."
However, Absolute would be concerned about Branson, or someone else, launching Virgin-branded ventures and competing with the company that had bought the original stations.
There is also the added complication that the rights to use the Virgin brand in connection to radio are limited to a UK licence only.
A senior source from a rival company said: "Essentially, the buyer will be purchasing a radio station that can't have a global strategy, which will present extra difficulties when trying to develop a broadband strategy for the stations."
A senior agency source added: "If the purchaser loses the brand name Virgin, then it will be a disaster, full stop. It will have to build up the whole brand equity from scratch, which will cost millions of pounds."
Absolute Radio said it was unable to comment on the matter.