In a statement on Thursday, the ICC said its executive board would discuss any possible return of Zimbabwe to Tests in November.
A series of one-day rule changes suggested by its cricketing committee and the choice of a vice-president to take over as president in 2008 are also on the agenda.
Last month the cricketing committee opposed the return of Zimbabwe to Test-playing status.
The Zimbabwe government withdrew the team from Test cricket last year after many experienced players quit the team due to differences with the national board. Zimbabwe still take part in one-day internationals and played in this year's World Cup.
Last month, the Australian government ordered the world champions to cancel a planned tour of Zimbabwe in protest against the policies of President Robert Mugabe.
The cricketing panel has also recommended changes to one-day rules such as introducing a free hit for the delivery following a front-foot no-ball.
The chief executives committee will meet for two days from Sunday and the board for the next two days before the annual conference on June 29.
The tussle for presidency is between Indian board chief Sharad Pawar and England board chairman David Morgan.
The issue assumed added urgency after South African president Percy Sonn died last month with a year left in his term. His compatriot Ray Mali was named acting president in the absence of a vice-president.