"There are just too many factors to consider for South Africa," the department of sport and recreation said in a statement on Friday.
Morocco, the original host of the African Cup scheduled for January and February, wants it postponed because of Ebola and may give up the tournament completely.
Tournament organizer the Confederation of African Football approached South Africa, Ghana and other countries to be on standby if Morocco withdraws.
But it's possible that no one else wants it because of the limited preparation time, and the threat of the deadly disease spreading through tens of thousands of travellers heading to the three-week, 16-team event.
South Africa's sports ministry stressed it had not yet been officially asked by the South African Football Association to consider hosting the tournament, but referred to the "Ebola challenge engulfing the continent."
More than 4,500 people have died in West Africa in the worst recorded outbreak of the virus. The outbreak is still not contained in the three countries worst affected: Liberia, Guinea and Sierra Leone. Ebola has no known cure or vaccination.
Morocco asked for the Jan. 17-Feb. 8 event to be postponed because of the threat of Ebola arriving with football supporters and others from affected regions. But CAF insisted it must go ahead on those dates or it will find another country.
The South African sports ministry said the cost of an unplanned hosting in just three months was its "major concern," but Ebola was a factor.
"The tournament ... may also pose a challenge on how we can grapple with the Ebola challenge engulfing the continent at the moment."
South Africa is one of seven countries to be approached as possible stand-in hosts, South Africa's football association said, but it would make no commitment until the outcome of meetings between CAF and Moroccan authorities early next month.
SAFA did, however, also point out worries over Ebola.
"We must all take care of this pandemic and put strict measures in place," SAFA President Danny Jordaan said.