The price could be as high as £9bn, though discussions with Li Ka Shing’s Hutchison Whampoa are at an early stage and there is no certainty a deal will be reached, the paper said.
O2, acquired by Spain’s Telefonica in early 2006, is second in the British mobile market with about 22m subscribers.
Hutchison already owns the fourth-largest mobile operator Three.
The UK telecoms sector is ripe for consolidation with the market split between four mobile network operators and four separately owned fixed line broadband providers.
Last month, BT entered exclusive talks to buy EE in a £12.5bn deal.
Hutchison dates back to 19th century colonial era Hong Kong and has been controlled by Mr Ka Shing for decades.
He has a fortune of $33.5bn, according to Forbes.
Mr Ka Shing’s other UK interests include Leeds-based Northern Gas Networks.