Sir Richard Branson is Virgin Media's largest shareholder

Carlyle may choose to distance itself from Sir Richard Branson and the Virgin empire to improve relations with BSkyB and Rupert Murdoch, the Observer said.

BSkyB has withdrawn its channels, including Sky One, from the UK cable group in a row over fees for services.

This followed BSkyB thwarting Virgin's efforts to take over ITV.

It seems odd.... especially as Virgin strikes a chord with the British public Industry source quoted in The Observer

Largest investor

Carlyle is considering whether it would be easier to restore a good relationship with Mr Murdoch if the connection with Sir Richard and the Virgin brand were severed, the paper said.

Quoting City sources, it suggested that the private equity firm would be able to swiftly settle the differences by making the move.

However one industry observer told the paper that about £25m had been spent on promoting the Virgin Media brand, which came into existence last year after a takeover of NTL.

"It seems odd that Carlyle is prepared to write that money off and start again, especially as Virgin strikes a chord with the British public," they said.

Sir Richard is the largest investor in Virgin Media, which has 9 million customers and a £4bn annual turnover, from its cable TV, internet and mobile phone businesses.

His 10% stake has grown by about £150m to be worth £577m since the takeover of NTL last Autumn.

He also owns the rights to the Virgin name.

Losses stemmed

If Carlyle's offer was accepted, the merger would value Virgin at approximately £5.6bn.

Virgin Media has been involved in a bitter dispute with Sky

The total value of the takeover deal, including Virgin's debt of almost £6bn, would be about £11.5bn.

If it goes through, it would be the second biggest takeover of a British business by private equity, after Boots.

It is believed Virgin's managers feel the business would be in a better position to grow as a private company, BBC business editor Robert Peston says.

In its last results, Virgin said it had three million users of its television services, 3.4 million broadband customers, 4.5 million subscribers to its mobile phone service and 4.1 million fixed-line telephone customers.

It has stemmed its loss of customers in the battle with BSkyB, saying that its number of viewers was "roughly flat" during April and May, thanks largely to promotion campaigns.

The company had earlier said it lost 46,900 customers in the three months to the end of March.