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 said to be in the running 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. The former cabinet minister's stint at the top of the BBC's governing body, which began in 2011, was due to end next April.