Lord Coe, the London 2012 chairman, said he had been approached to stand as the successor to Colin Moynihan.
A BOA committee is drawing up a list of candidates to replace Lord Moynihan, who announced last month he would be stepping down after seven years.
Lord Coe, who was recently made the UK's Olympics legacy ambassador, said: "I am happy for my name go to forward."
The 55-year-old, a 1500 metres Olympic gold medallist in 1980 and 1984, led London's successful bid for the 2012 Olympics and was subsequently made chairman of Games organiser Locog.
As legacy ambassador, he has been asked to advise Prime Minister David Cameron on how to best secure long-term benefits for the UK following the London Games.
Mr Cameron said Lord Coe had "done a brilliant job delivering the best Games ever", adding: "Now I want him to help me deliver the best Olympic legacy ever."
Sebastian Coe has confirmed he will stand to be the next chairman of the British Olympic Association (BOA).