Virgin Radio is part of the Scottish Media Group, the troubled media group that is in the process of selling its Herald newspaper business.
Reports suggest Virgin could be valued at as much as £150m or significantly higher, as SMG is thought unlikely to be willing to sell the station.
Desmond is known to be keen to expand his media empire and has looked at other, unnamed acquisitions, but favours buying the national Virgin Radio network above all others.
The move could see the break up of SMG, which is working out how to reduce its debts of £400m. With bids reaching £230m for its Herald newspaper titles, this would go a long way to cutting its debt, but it would still owe £200m.
As well as Virgin Radio, SMG owns the Scottish and Grampian ITV franchises and the cinema advertising company Pearl & Dean.
Questions have been raised about Desmond's ability to get funding for any such takeover deal. SMG bought Virgin Radio two years ago for £225m -- however, it has since fired its most famous DJ, Chris Evans, for failing to turn up at work despite being seen out on boozing sessions.
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