The Moroccan government made the plea to CAF to suspend the tournament, due to be held between January 17 and February 8 next year.
Ebola, a deadly virus, has killed thousands of people in recent weeks as it continues to spread in the west of the continent.
The virus has already affected qualifying, with several matches relocated.
On Saturday, CAF released a statement declaring that the tournament will not be rescheduled, explaining that the event had never been changed in the past.
But the statement did go on to say that CAF will meet with Moroccan officials next month to discuss the issue.
"The Confederation Africaine de Football (CAF) on Friday, 10 October 2014 received a request from the Ministry of Youth and Sports of the Kingdom of Morocco," it read.
"The letter was seeking a deferral of the schedule of the Orange Africa Cup of Nations Morocco 2015 fixed for 17 January to 8 February, due to the Ebola outbreak.
"CAF has registered the request and wishes to state that there are no changes of the schedules of its competitions and events.
"It must be noted that since the first edition in 1957, the Africa Cup of Nations has never witnessed a deferral or a change in schedule.
"CAF has also been cautions since the commencement of the final round qualifiers of the Orange Africa Cup of Nations Morocco 2015 on the health risks posed by the Ebola virus and has consistently applied precautionary principles, taking into account the recommendations of the World Health Organization and various medical experts.
"The request of the Moroccan party will be discussed at the next meeting of the CAF Executive Committee scheduled for 2 November 2014 in Algiers, Algeria, on the sidelines of the second leg of the 2014 Orange CAF Champions League final.
"Subsequently, a meeting will be organized between CAF and the Moroccans in Rabat on 3 November 2014 and the CAF delegation will be led by its President, Issa Hayatou."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.