Cable operator Liberty Global, which owns UPC in Ireland, may move for Telefonica's €700m-valued Irish O2 business.
Spanish firm Telefonica is understood to have identified the O2 Ireland business as an asset that could be sold to reduce the company's €51.3bn debt mountain.
Last week, Telefonica executives told investors that Ireland was a market that "could benefit from consolidation".
Telefonica is seeking to reduce its debt by around €4.3bn this year. Last month it sold a 40 per cent stake in its Central American operations and the Spanish firm is also believed to be reviewing its stake in Czech and China Unicom (Hong Kong) units.
"We are managing our portfolio, aiming to increase the value of the businesses where we are present. We are not in an expansion mode, but yes, we can be in a strengthening mode in some the markets where we operate.
"Some of those markets could benefit from a market consolidation. And there are several examples, chief operating officer Jose Maria has spoken about one of them before. Ireland could be another one," said Angel Vil, Telefonica's chief financial and corporate development officer, last Wednesday.
A Telefonica spokesman said they did not comment on speculation.
Three has been an active dealmaker in the European market, with buyouts in Austria expected to be followed by a move for Telecom Italia.
Private equity group Blackstone, which owns close to 20 per cent of Eircom, is also believed to have examined the possibility of buying O2.
However, this would be complicated by regulatory and competition hurdles.
Last week, Liberty Global president Mike T Fries told investors that the company may look at mobile assets in Ireland.
"I think you'll see a consolidation within mobile, within markets and across markets. I think you'll see consolidation among fixed-line operators within markets, potentially.
"And you have seen that, by the way, within markets, with most resellers going out of business or being bought up, and across markets. And I think you'll see cable play a very important role, both within markets, across markets, and across sectors," Fries told investors last week.
"We've looked at cable and mobile assets in the past. We looked at the Swiss mobile asset. We may or may not look at the Irish mobile asset. There are massive synergies to be achieved in that regard.
"We have a better business; no question about it. So, for us, we have to be absolutely convinced that getting into the mobile business in whatever way is accretive, because our core business is absolutely solid. But I do think you'll see things, activity across the spectrum there," he added.
"We're committed to continually improving our products and services. Our style is to make announcements at appropriate times, not predictions. So until we're ready to launch with a service we will not be revealing our plans about mobile or MVNO in Ireland," a UPC spokeswoman told the Sunday Independent.