Lord Alli is understood to believe that Virgin Radio, which broadcasts nationally on AM and in London on FM, could be improved with better content and marketing.
Virgin Radio reaches 2.46m listeners nationally, according to the latest Rajar figures covering the October-December 2004 period. This was a fall of 5.3% from 2.6m in the previous quarter.
It has emerged that Lord Alli put together a management team backed by private equity group 3i and met with SMG chairman Chris Masters in December.
He said the offer represented a fair price that valued Virgin Radio at £85m with a £15m bid premium.
According to Lord Alli, Masters made it clear that he would not sell, no matter what the price was, and he was going to appeal directly to SMG's shareholders.
These include ITV, which has a 17% stake in the Scottish broadcaster, and was itself rumoured to be interested in buying Virgin Radio. In October, it paid SMG £31m for its 25% stake in GMTV.
Emap has also been linked to Virgin Radio in the past, but is believed to be focusing on taking control of Scottish Radio Holdings, in which it has a 27% stake.
SMG originally paid £225m for Virgin Radio in 2001. It also owns Scottish TV, Grampian TV, Ginger Television and outdoor advertising sales house Primesight and cinema ad firm Pearl & Dean.
Lord Alli made his fortune by co-founding Planet 24 with his business partner Charlie Parsons and Live Aid and Band Aid organiser Bob Geldof. The company produced Channel 4's seminal morning show, 'The Big Breakfast', which helped build the careers of presenters Chris Evans, the late Paula Yates, Johnny Vaughan and Denise Van Outen.
The trio sold Planet 24 to Carlton in 1999, and Lord Alli was briefly managing director of Carlton Productions, resurrecting the daytime soap 'Crossroads', which has since been axed.
A second-generation Guyanese and New Labour fixer, Lord Alli was made a peer in 1998.
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