Almost five million households in the UK subscribe to Virgin's broadband, television and landline services.
Virgin also has some three million mobile phone customers in Britain.
Sir Richard Branson owns a three percent stake in Virgin Media, which is listed in New York, with a secondary listing in London.
The company's share price soared on news of the talks, going up by some 18% in trading.
US-based Liberty Global operates in 13 territories and is seeking to expand its base in Europe.
The talks were confirmed by Virgin Media, which currently has debts of around $9bn (£5.7bn), in a brief statement.
It also owns a content and channels group called Chellomedia.