The owner of The Daily Telegraph, the British media outlet, said on Saturday it was in advanced talks to sell itself to a major rival, a move that would further consolidate the country’s news media. Telegraph Media Group said it was finalizing terms of a deal to be sold to DMGT, the owner of The Daily Mail, the country’s biggest newspaper by circulation, for 500 million pounds, or $655 million. The talks came a little over a week after The Telegraph said a previous suitor, the American investment firm RedBird Capital Partners, had walked away from its own £500 million takeover bid. “The Daily Telegraph is Britain’s largest and best quality broadsheet newspaper, and I have grown up respecting it,” Jonathan Rothermere, the chairman of DMGT and a scion of its founding family, said in a statement. “It has a remarkable history and has played a vital role in shaping Britain’s national debate over many decades.”