The ICC had received the nominations of England and Wales Cricket Board Chairman David Morgan and Indian board president Sharad Pawar, it said in a statement. The deadline was Dec. 31.
A nominations committee will make its recommendation at the next ICC executive board meeting in March.
The board will then make its recommendation to the ICC annual conference in London in June where a vote will be held. A candidate must secure the support of two-thirds of the 10 full members or Test-playing nations to be elected.
Sonn began his two-year term in July last year and the ICC has the option of extending it to a third year. His successor will take over in 2008 if the ICC elects not to exercise that option.