Davies, according to reports in the Sunday Business newspaper, was the only name on a shortlist presented to the prime minister Tony Blair and culture secretary Tessa Jowell. They are expected to formally approve his appointment later this week.
He takes over from Sir Christopher Bland, who controversially retained the job while also being chairman of BT. Sir Christopher was named BT chairman in April and it was agreed he would hold both posts until a new BBC chairman could be found.
Davies, who is also deputy chairman of the BBC, was an early frontrunner for the top BBC job despite concerns that his appointment would be seen as cronyism.
Davies is a prominent support of New Labour and his wife, Sue Nye, is chancellor Gordon Brown's secretary.
However, it is believed the government will offset charges of cronyism with the appointment of another economist and Conservative supporter, Lady Sarah Hogg, as deputy chairman. It is believed this combination has already been given approval by the new Conservative leader Iain Duncan Smith.
The closest contender to Davies for the job was current BBC vice-chairman and senior BBC presenter David Dimbleby. The full shortlist also included: Baroness Jay, former leader of the House of Lords; BBC governor Dame Pauline Neville Jones; former Channel 4 chief executive Michael Grade; and former British Library chairman John Ashworth.
BBC director general Greg Dyke is said to get on well with Davies. However, Dyke has denied that he said he would quit if Dimbleby had been given the job.
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