Several people familiar with the situation told the Financial Times that a bid could be announced in the coming days more than five years after Liberty first considered buying the company.
Such a deal would put Liberty owner John Malone in direct competition with his former partner Rupert Murdoch, controller of BSkyB, which also offers triple play TV, broadband and telephone services.
The publication said that a deal had not yet been finalised and could still fall apart.
In a statement today Virgin Media confirmed that talks were taking place and said a further announcement would be made in due course.
“Virgin Media confirms that it is in discussions with Liberty Global, a leading international cable company, concerning a possible transaction. Any such transaction would be subject to regulatory and other conditions.”
Virgin Media shares closed at $38.69 on Monday, giving the cable operator a market capitalisation of $10.4 billion.
Liberty has been active in the European market, having increased its stake in Belgium’s Telenet to 58% after a failed buyout offer last year.
Acquiring Virgin Media could provide synergies with Liberty's other European operations in terms of set top box and telecoms equipment orders.
The UK broadband market is fiercely competitive with BT Group, Virgin, BSkyB and TalkTalk fighting for subscribers. According to Ofcom, the sector grew 8% in 2012, with subscribers estimated to total approximately 22 million.
Sir Richard Branson’s Virgin Group owns just under 3% in Virgin Media but receives a percentage of the company’s revenue, worth approximately £10 million, as a royalty payment each year.