According to a report in the Sunday Times there have been 11 expressions of interest for the group, which has around 3.3m customers.
The news follows reports earlier this month that US private equity giant Carlyle could buy Virgin Media and drop the connection to Richard Branson in an effort to repair relations with Rupert Murdoch's BSkyB.
The Carlyle group is one of the interested parties with others including a consortium including Kohlberg Kravis Roberts, Providence Equity Partners, Blackstone, Cinven and Apax.
Private equity is not the only corner interested in buying broadband, TV and phone group Virgin Media, US media giants Viacom and Time Warner are also reported to be interested.
The auction follows Virgin Media losing of a number of subscribers to rival Sky, after the spat that saw the satellite group pull its basic package, which included access to shows such as '24' and 'Lost'.
Branson owns 10% of the shares following the merger of Virgin Mobile with what was then NTL, which created the UK's first quad-play media company which offers customers TV, mobile, broadband and a landline in one package.