In a statement to the stock exchange this morning, the company said all discussions are at a "highly preliminary stage", adding that it is "continuing" to develop plans for its own mobile networks.
BT demerged O2 - then known as BT Cellnet - along with a number of its other businesses in 2001. In 2005, it was bought by Spanish operator Telefonica for £17.7bn.
The company said it had "received expressions of interest from shareholders in two UK mobile network operators, of which one is O2, about a possible transaction in which BT would acquire their UK mobile business".
After BT span off O2, it was quickly seen as a terrible strategic decision as mobile became increasingly popular among consumers. In recent years, the company has been attempting to widen its market, with a renewed focus on high-speed broadband, plus a recently-launched pay-TV offering which has been regarded as fairly successful.
In 2013, O2 sold its broadband operation to Sky for £200m.
Shares in Telefonica had risen 1.4 per cent in mid-afternoon trading.