A cash deal of more than £10bn could lead to the creation of the UK's largest mobile phone operator, with Three taking over O2.
Three's parent, Hutchison Whampoa - owned by the richest man in Asia, Li Ka-Shing - said it was in "exclusive negotiations" with Telefonica to buy the UK's second-largest mobile firm for £10.25bn.
Hutchison confirmed in its statement that it had offered £9.25bn, with a deferred further payment of up to £1bn after completion of the deal but it said any agreement would be subject to due diligence and regulatory approvals.
Any tie-up would be likely to interest industry authorities as it would reduce the number of players in the UK mobile phone market to three - hitting competition - despite the possibility of both brands remaining.
The telecoms watchdog, Ofcom, could demand that Three and O2 hand over some spectrum capacity to rivals.
A combined player would create a company with a current market share of around 40% - with 31 million customers between them.
Three, which is currently the smallest of the UK's mobile operators in terms of market share behind Vodafone, has been setting lower price tariffs in a bid to attract new customers and grow its stable.
EE - which is the current market leader with 32% - is on the verge of being snapped up by former O2-owner BT in a deal worth £12.5bn.
BT is bidding to become a so-called "quad play" provider by bundling home phone, mobile, TV and broadband services together in a single package.
Its proposed deal with EE sparked a frenzy of speculation about whether other players in those markets would look to follow suit through either acquisitions or partnerships.
Telefonica's willingness to part with O2 was seen as acceptance that it did not want to enter the quad play arena in what is a declining mobile phone market.
It is widely believed to be looking at emerging markets to achieve growth.
