Morocco is holding fast to its request two months before the tournament is to kick off on January 17, but CAF insists it is not up to the host country.
The federation could impose a fine and suspension of Morocco’s national team if it does not reconsider.
In the meantime CAF has scrambled to find another host country on short notice, without any indication yet that any have accepted.
The federation’s executive cNations Cupmmittee began the two day meeting at its headquarters in Cairo, and could announce its decision on Tuesday or Wednesday.
“There are 15 points on the agenda. One of them is the African Cup 2015,” CAF spokesman Junior Binyam told AFP before the meeting started.
Morocco had said its call for a postponement was “dictated by health reasons of the most dangerous kind, linked to the serious risk of the spread of the deadly Ebola pandemic.”
The deadly ebola virus has killed at least 4,960 people, mainly in the West African countries of Sierra Leone, Liberia and Guinea. Morocco fears that an influx of foreign fans could help spread the epidemic.
CAF has said the fears are exaggerated and that only a limited number of foreign fans will go there.
The Ebola epidemic first hit the Cup of Nations in August when Seychelles forfeited a qualifying tie rather than host a return match against Sierra Leone.
As the death toll mounted, CAF barred Sierra Leone and Guinea from hosting their qualifying group games.