The body is expected to vote on admitting the two nations into the elite group that is permitted to play in the traditional five-day Test matches.
If approved, Ireland and Afghanistan would take the total of countries playing Tests to 12.
Until 1982 there were only seven Test-playing nations but that year Sri Lanka were admitted, Zimbabwe then joined in 1992 and Bangladesh became the most recent member in 2000.
West Indies crawl over the line in low-scoring encounter
Cricket has a long history in Afghanistan but the country played amongst the sports minnows until gaining one-day international (ODI) status in 2011.
Two years later the country, still suffering from the impact of war and conflict, was given 'associate member' status of the world governing body ICC.
Afghanistan hope for more ODIs after drawing West Indies series
In 2015, Afghanistan played in their first 50-over World Cup and they have also featured in the World T20 competition.
Ireland have steadily progressed in the game and first qualified for the World Cup in 2007 when they pulled off a shock win over Pakistan and they have qualified for both World Cups since.
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