Industry insiders claim that under the terms of Virgin Group's contract with SMG, the former can revoke the use of its brand in the event of a merger. It is understood that the clause specifically relates to firms that are seen as competitors to the Virgin Group, which has a wide presence in the media sector. SMG acquired the radio station after buying Ginger Media Group for £225m in 2000.
SMG is currently operating without a permanent chief executive and has halted its search for one during the merger process.
Fru Hazlitt had been a frontrunner for the position, before resigning as Virgin Radio's chief executive earlier this month. She has since been linked with a variety of roles at rival radio media group GCap Media.
Hazlitt is thought to be talking to Ralph Bernard, chief executive of GCap Media, about becoming managing director of GCap London, which would put her in charge of Capital 95.8.
Beleaguered GCap has already drafted in former RAB chief executive Douglas McArthur on a consultancy basis in its commercial department.
A spokesman for SMG said he could not comment on the merger.