The Spanish telecommunications giant has already laid the groundwork for a potential IPO of O2 and is also considering other options.
The company would remain the main shareholder in all of the options that are being considered.
Earlier this year, the European Commission blocked the company's sale of O2 to CK Hutchison by arguing that the deal would artificially inflate prices and offer fewer choices for UK customers.
When the commission rejected the deal, its value was estimated at about $14bn.
Since then, Telefonica has been searching for alternative options to pull the company out of debt.
Telefonica chairman Jose Maria Alvarez-Pallete was quoted by Bloomberg as saying, “We have been working to list it, so if today or in the next few weeks we decided to do so, we could do it by year’s end.”
The Spanish firm said in a separate regulatory filing that it is launching an IPO of its Telxius infrastructure unit, with a free-float of about 25%.
The IPO is expected to take place before the end of this year, after the company secures regulatory approval for the deal.
Telefónica created Telxius in February this year to manage its infrastructure assets including telecommunication towers in Spain and other countries and 31,000km of fibreoptic submarine cables.
Telxius has since then expanded its portfolio, notably via the acquisition of 2,350 mobile masts in Germany.
The company’s proforma revenue was €691m in 2015, with operating income before depreciation and amortisation of €323m.