He said: "I did allow my name to go forward to give myself time to properly analyse whether I had enough time to do the job to the best of my abilities.
"On reflection, I haven't the capacity and I now want to concentrate on my current commitments and the International Association of Athletics Federations (IAAF) election."
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 Coe received a special award at Buckingham Palace today for his role as chairman of London 2012.
The two-time Olympic champion was made a member of the Order of the Companions of Honour by the Princess Royal during an investiture ceremony.
He said: "It's a lovely honour and I'm deeply flattered.
It is really a recognition for the extraordinary work of so many people: our teams at Locog, the most talented, focused people I've ever worked with - and the people of Britain whose generosity of spirit helped get us across the line."
The Order consists of the sovereign and 65 ordinary members and recognises service of national importance.
Previous recipients include scientist Professor Stephen Hawking, naturalist Sir David Attenborough and painter David Hockney.
Boris Johnson and Seb Coe both denied my suggestion that they were the next Prime Minister and Mayor of London respectively.
Lord Coe later joked that politics "left him in a very big way in 1997," referring to that year's general election in which he lost his seat for Falmouth and Camborne. Perhaps the voters would feel a bit warmer towards him now.
Seb Coe has done a brilliant job delivering the best Games ever. Now I want him to help me deliver the best Olympic legacy ever. Legacy has been built into the DNA of London 2012 from the very beginning thanks to Seb. I'm delighted that (IOC president) Jacques Rogge described our legacy plans as a blueprint for future Games hosts.
I am determined to make the most of the economic opportunities on offer from hosting the Games - making sure that we turn these Games into gold for Britain. I cannot think of a better person than Seb to be our ambassador to the global market-place and make sure we achieve our ambitious legacy targets.