Virgin put VMtv up for sale in March in order to reduce its debt burden. The channels currently consist of Bravo, Bravo 2, Living, Living 2, Challenge, Challenge Jackpot and Virgin One.
In addition to there are a number of bidders in the frame, including Channel 4, Time Warner, RTL and NBC Universal.
BSkyB's high bid has raised eyebrows in the industry as the broadcaster previously described VMtv as worthless when it was in dispute with Virgin over how much they would pay to host each other's channels.
There has been speculation that BSkyB's aim in bidding so high is simply to ensure the channels stay out of the hands of rivals such as Channel 4 or, failing that, see those rivals pay the maximum price to obtain them.
But despite the strength of the offer it is questionable whether Virgin will sell to BSkyB, its main rival in pay-TV delivery.
Once VMtv is sold, Virgin is also expected to sell its stake in UKTV, which includes Dave and Gold. As joint venture partner, BBC has first refusal on the channels.
If Channel 4 succeeds in buying VMtv, it is believed to be considering folding the channels into a joint venture with BBC Worldwide.
VMtv is home to such shows as 'CSI: Crime Scene Investigation', 'The L-Word' and 'Britain's Next Top Model', which all air on Living, while Bravo, which is billed as Virgin's channel for men, airs shows including the David Mamet-created 'The Unit', which stars Dennis Haysbert.