The Spanish owner of O2 said it may float the British mobile network after seeing a tie-up with rival operator 3 collapse.
Telefonica said it had started exploring strategic options for the UK business, including the possibility of an initial public offering (IPO).
But it said it would continue to hold a majority shareholding in the business if any such move took place.
The update comes as Telefonica announced it would also float infrastructure subsidiary Telxius Telecom in the second half of this year.
It will be listed on the Barcelona, Bilbao, Madrid and Valencia stock exchanges and included on the Spanish Continuous Market.
The European Commission formally blocked Hong Kong-based mobile operator CK Hutchison, which owns 3, from pushing through a £10.3bn (€12.2bn) takeover of O2 in May.
EU antitrust regulators argued that the deal would have meant higher prices and less choice for UK consumers.
European regulators had been studying the deal for several months after CK Hutchison and Telefonica entered into exclusive talks in January 2015.
O2 has around 28.5% of the UK market, but a merger with Three's share of just over 8% would have seen it climb to become the biggest operator in the UK.