Its president Giles Clarke has been an implacable opponent of an Olympic attempt.
The ICC's chief executive Dave Richardson straddled the fence.
In terms of developing the game into fresh territory "it would probably be a good thing if cricket was in the Olympics", he said.
However, there would be immediate difficulties when considering just who competes at the Olympics. It would by necessity have to be a T20 tournament and surely there's enough of them around the game already, headed, as Richardson pointed out, by the world championship.
But more relevantly, it would take place during an English summer, and in any case neither England nor the West Indies would be eligible to compete under those titles. It would be Britain and the range of nations who only come together for international cricket.
Those supporting an Olympic push may feel buoyed by the inclusion of golf and rugby sevens for next year's Rio Games.
Golf does not belong.
Reason one: Many of the best players in the game will not be in Rio due to the qualifying criteria laid down. The idea is to get a spread of countries there, which is extremely Olympian but will produce devalued fields.
Reason two: An Olympic medal should be a sporting pinnacle. Find one player who would prize an Olympic gong over a major title. Didn't think so.
In New Zealand and a handful of other countries the inclusion of sevens was greeted as a serious chance for a medal. But forget the spruiking in certain parts of the world. It does not compare with a pile of other sports in terms of worldwide appeal.
Cricket has enough on its plate, good and bad, to occupy itself. This suggestion should be quickly consigned to the large round bin.