London mayor Boris Johnson is backing Olympics supremo Seb Coe as his replacement.
Johnson has told friends he believes he can persuade Coe to become the Tory candidate in 2016.
The former Olympic champion and boss of the London 2012 games has so far resisted efforts by the party to persuade him to join the race for City Hall.
Instead, Coe has set his sights on becoming the President of the governing body of world athletics, the IAAF.
Lord Coe launched his campaign for the IAAF presidency last month. But he faces a formidable challenge from former Ukranian pole vaulter Sergey Bubka.
The result of the IAAF vote will be known in August 2015.
If Coe can be persuaded to stand for City Hall it raises the intriguing possibility of a two-horse race against his friend and former Olympics minister Dame Tessa Jowell who hopes to be Labour's candidate.