The Spanish firm's chairman Maria Alvarez-Pallete said: “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, if markets were right."
He said there was no obligation to do so if market conditions changed, however. The company will decide on a course of action in the coming weeks, and a private sale is also still on the cards. Several private equity firms are said to be interested.
The telecoms firm also announced its intention for a partial listing of its infrastructure unit Telxius on the Spanish stock market by the end of the year.
Both listings were put on the back burner in light of the EU referendum vote in June.
The EU competition commission poured cold water on the £10.25bn sale of O2 - which would have merged with Hutchison's UK network Three - in May as it would have reduced competition in the market according to the watchdog.
Telefonica is seeking to reduce its debt pile with the listings.
What you need to know