Hutchison Whampoa, controlled by Hong Kong magnate Li Ka-shing, is considering a bid of up to £9bn for O2, according to the Sunday Times, citing anonymous city sources.
According to the report, Three's owner is currently in early-stage talks and there is no guarantee a deal will go ahead.
A merger could spell the end of the Three brand, since the firm is both younger and smaller than O2. The upstart operator has won over the millennial generation with viral campaigns, such as the moonwalking Shetland pony, cheap tariffs and all-you-can-eat data plans.
The deal would mark further consolidation in the mobile market after BT entered exclusive talks to acquire EE for £12.5bn towards the end of last year. It was thought O2 was BT's original acquisition target.
It isn't clear whether regulators would clear the acquisition, since a merged O2 and Three would create the biggest mobile network in the UK.
Should both deals go ahead, UK consumers would have a choice between just three main operators - Three/O2, EE/BT and Vodafone.
According to Kantar Worldpanel analyst Imran Choudhary, the shake-up could prompt more consolidation.
He said: "Rumours that Three is looking to acquire O2 from Telefonica come as no surprise, given the need to protect themselves from a new BT/EE partnership.
"The big loser from the deal would be Vodafone, which would suddenly find itself one of the smallest players in the market, no doubt speeding up its plans to potentially acquire Virgin Media, Sky or TalkTalk."
Telefonica, O2's parent company, has not returned a request for comment.