The Observer claims to have seen a private document titled 'Project Coaxial' showing that Blackstone, Cinven, KKR and Providence are prepared to approach Virgin Media, although the document did not offer any information about the timing of the proposed offer.
The price is substantially lower than the $11bn Virgin Media was valued at when it put itself up for sale in July last year, following an approach from another private equity firm, Carlyle.
The auction process was derailed by the credit crunch, which severely restricted the ability of private equity bidders to borrow enough debt to fund acquisitions.
Since July, Virgin Media's share price has descended from $29.39 to its Friday night close in New York of $13.93, just off its January low of $13.35. This makes it worth $4.6bn, while it also has debt of around $11bn.
Virgin brand owner Sir Richard Branson has a 10.5% shareholding in Virgin Media, and would stand to receive $600m-$750m if a deal were to be done.
Last week, it was reported that Virgin Media is carrying out a review of its TV channels, including Living TV, Bravo and its half share in UKTV. The move could trigger interest from rival companies, including BSkyB, ITV and Five owner RTL.
The reports came as the company confirmed Neil Berkett was to take over as chief executive officer, having held the position on an interim basis for more than six months following the departure of Steve Burch.