The Financial Times cited unidentified sources familiar with the matter as saying O2 would be the first European mobile operator to reach an agreement with Apple for iPhone in one of the industry's most sought-after deals in years.
The Times newspaper, without citing sources, said the final contract was expected to be signed imminently.
An O2 representative had no immediate comment. Telefonica declined to comment.
Apple began selling the iPhone, which combines a wireless phone with music- and video-playing capabilities and Web browsing, in the United States on Friday in the most highly anticipated technology product launch so far this year.
A deal with Apple would be a big boost for Telefonica, which bought O2 for 17.7 billion pounds ($35.7 billion) in 2005. It would be a blow to British rival Vodafone, which had hoped to get the contract.
O2 is the biggest mobile operator in Britain, in terms of subscriber numbers, with about 18 million customers, but it trails Vodafone in terms of revenue market share.