Sir Richard Branson, Virgin Media’s biggest shareholder, is open to a buyout of the cable group, paving the way for a potential deal at $10 billion (£4.9 billion) or more.

As The Times revealed on Saturday, Carlyle, the private equity group, is circling the television and telecoms group. The interest has kicked off an auction process in which Sir Richard, whose Virgin Group holds 10.5 per cent of the $8 billion Virgin Media, will play a critical role.

City sources said that Sir Richard was willing to weigh up any offer. It is believed that potentially he could seek to roll over some of his stake into a new entity. It is not clear at this stage what size of stake the billionaire entrepreneur would retain. Virgin Group declined to comment yesterday.

The latest negotiations for the communications group — whose turbulent history included a life-saving restructuring in 2002 — are believed to centre on a price above the $30 per share that was informally pitched to Virgin Media by a consortium of private equity players last year. A $30-a-share bid equates to an equity value of about $10 billion.

That previous approach, by players including Providence Equity Partners, Kohlberg Kravis Roberts and Cinven, failed to result in a deal because of opposition from key shareholders in Virgin Media, including Bill Huff, the influential New Jersey hedge fund owner. Today Mr Huff is far lower down the group’s share register, with only 4.9 per cent.

In addition, a key Huff ally, William Connors, who used to work with him in his hedge-fund business, recently stepped down from the cable group’s board after claims that Mr Huff had too much influence.

The latest takeover attempt comes after disappointment that the merger last year of NTL:Telewest and Virgin Mobile has failed to create the formidable force in home entertainment that had been hoped for. Since the deal the group has struggled to show the benefits and its Nasdaq-listed shares closed on Friday at $24.37.

Despite a £25 million branding campaign featuring the Hollywood actress Uma Thurman, the group lost nearly 47,000 customers in the first quarter of this year and became embroiled in a protracted legal dispute with BSkyB, in which News Corporation, the parent company of The Times, has a 39.1 per cent stake.

The continued failure to fulfil its perceived potential has put pressure on Stephen Burch, Virgin Media’s chief executive.

However, people familiar with Virgin Media are said to feel that having integrated its various parts, the group is now in a much stronger position.

In talks with potential buyers, Virgin Media is likely to emphasise that its advertising campaign has yet to feed into its results. In addition, it is likely to highlight recent figures from Ofcom, the regulator, showing that take-up of cable in Britain has hit its highest level for almost five years.

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