London 2012 supremo Lord Coe has refused to rule himself out of the running to replace Lord Patten at the top of the BBC Trust.
The former Olympic champion, who sits in the House of Lords as a Conservative peer and was an MP for five years, is said to have the support of the Government to take the role.
He told Victoria Derbyshire on BBC Radio 5 live that it was " a very meaty job".
Asked if he would apply, he said he was "not sure" and added that he had "a few weeks to think about it".
Lord Coe said he had not been approached formally, but added: "I have conversations about all sorts of things all the time, I'm not going to maintain a running commentary on that."
He said his politics were "clear and a matter of public record" but added he had " always been highly independent in everything I've ever done".
Other names mentioned in relation to the role at the BBC's governing body include Dame Marjorie Scardino, the former chief executive of the company behind the Financial Times, and Channel 4 chairman Lord Burns.
Lord Patten stood down in May for health reasons after a turbulent three years in the job.
The former cabinet minister's stint at the top of the BBC's governing body, which started in 2011 and was due to end next April, has seen him work with three different director-generals and weather controversies including executive pay and the corporation's Diamond Jubilee coverage.
Lord Patten, who had heart surgery seven years ago, said he stepped down "on the advice of my doctors".
Former BBC executive Roger Mosey, who masterminded the corporation's Olympics coverage, welcomed the news w hen Lord Coe emerged as a possible replacement last month but said reform was needed.
Mr Mosey, whose career at the BBC included stints as editor of the Today programme, controller of Radio 5 live and head of television news, said: "Seb Coe would be a great choice as BBC chairman. But the Trust role as now constituted is undoable: can't be both regulator and cheerleader."