Telecoms giant BT is in talks with Telefonica about buying the O2 mobile network from the Spanish firm.
"All discussions are at a highly preliminary stage and there can be no certainty that any transaction will occur," said BT.
In 2002, BT spun off O2, then called BT Cellnet. In 2005 it was acquired by Spain's Telefonica for £17.7bn.
BT said it had also been approached by the owners of another network, believed to be EE, about a UK buy-out.
Richard Hunter, head of equities at Hargreaves Lansdown stockbrokers, said it was a sector "ripe for consolidation".
However, he added: "I think there would be some kind of irony that they would effectively be buying back a business that they previously had."
Its value is around half that paid by Telefonica. Deutsche Bank values O2 UK at £9bn, while UBS values it at £9.6bn.
EE's owners - France's Orange and Germany's Deutsche Telekom - put plans for an initial public offering of EE on hold this year. They said recently that their strategies in the UK would depend in part on how aggressively BT went into mobile.
"This could be the moment that commitment to the UK mobile market finally cracks and we see parent companies starting to exit," Citigroup analysts said in a note, adding that UK profit margins were very low compared with other markets.
A takeover of either O2 or EE would create a communications giant covering fixed-line phones, broadband, mobile and TV.
According to Citigroup, EE holds 33.8% of the UK mobile market by revenue, and O2 some 26.2%.
BT has about a third of the home broadband market. Analysts suggest that customers increasingly want to buy their fixed-line and mobile services from one company.
Michael Bishop, analyst at RBC Capital Markets, said: "With two operators potentially looking at selling their mobile asset... we believe BT is in the driver's seat and the risk of overpaying for a mobile asset is reduced."
BT's TV channel BT Sport is engaged in a viewership battle with Sky, as it tries to lure broadband customers with Premier League broadcasts, and it has also bought the rights to Uefa Champions League games.
By the close, UK trade, BT's shares were up by 14.10p, or 3.71%, at 394.10 pence.
In a statement to the Spanish stock market, Telefonica, said: "Telefonica informs that, although it is in talks with British Telecom, these talks are in a highly preliminary phase and there is no certainty that a transaction will take place,"
Last year, Telefonica sold a number of assets in order to reduce debt and improve its credit ratings.