World Test and One-day International champions leave on Thursday for Africa to play what is likely to be an outclassed second-string Zimbabwe team.
This follows the Zimbabwe Cricket Union (ZCU) firing of 15 white players who were in conflict with the Board over selection issues.
Local daily The Australian on Wednesday reported May would meet with ICC operations manager Dave Richardson in Dubai on Friday hoping the game's governing body can resolve the Zimbabwe situation which has drastically weakened the African team.
May, the chief executive of the Australian Cricketers Association and the Federation of International Cricketers Associations, believes if the crisis continues the ICC must ditch the program which demands all 10 Test-playing nations play each other regularly.
"If this cannot be resolved, the program should be thrown out and the top six nations should play against each other," May told The Australian.
While there are penalties running into millions of dollars for teams that do not agree to play home-and-away matches against every other Test nation twice in a 10-year period, there is nothing that demands a country must field its best team.
"There must be quality controls to maintain the standard of Test cricket," said May. "This (crisis) makes cricket look stupid."
May, a former Test off-spinner, left Australia late Tuesday for Dubai.