Patel indicated his decision in a telephonic conversation with ICC President-Elect David Morgan on Sunday.
The ICC named Patel as their preferred candidate to succeed Malcolm Speed but the South African has opted to continue as chief executive of broadcaster SuperSport.
The Recruitment Committee – ICC President Ray Mali, Creagh O"Connor, and Vice President Sharad Pawar – will now reconvene to elect new CEO.
Once the Recruitment Committee has identified a preferred candidate, it will make a recommendation to the ICC Board with a view to confirming the appointment at the earliest opportunity.
The incoming CEO will take over from Speed, who steps down from the role after this year"s ICC Annual Conference, which will take place between 29 June and 4 July.