The Labour peer Lord Alli, with backing from 3i, is attempting to buy Virgin Radio from SMG and has already had a £100 million offer rejected.
Virgin licensed its name to the station eight years ago when it was bought by Chris Evans and according to reports may have the right to veto Lord Alli's bid.
Branson's advisers are said to be keen to find out how much money Alli and his team intend to invest in the station if they gain control because of concerns over the effect a takeover may have on the Virgin brand.
Alli and his team are now attempting to gain the backing of SMG shareholders for a new bid.
Separately, Virgin Radio's hunt for a chief executive to replace John Pearson is hotting up.
Reports suggest that candidates for the job include Shaun Gregory, Emap Performance's managing director of national brands and Nathalie Schwarz, the former Capital Radio director of strategy.
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