There have been suggestions that the Confederation of African Football will postpone the tournament, which is due to be held in Morocco next year.
"I really wish it doesn't happen with all the people that will be moving around," the Daily Mail quotes Enyeama as saying. "But I'm not CAF. I'm not the one who calls the shots."
More than 4,000 people across West Africa have died from the virus following the recent outbreak.