The 2022 World Cup hosts had not been "officially asked to host" the continental tournament after Morocco was stripped of the right to stage the event, said Sheikh Hamad bin Khalifa bin Ahmed al-Thani in a statement.
"If officially asked, Qatar is ready to offer any help in hosting the African Cup due to its strong relation with Issa Hayatou, president of the Confederation of African Football (CAF)," he added.
The decision "concerns CAF, which all world football authorities are expected to support", he said.
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He recalled that his country had already organised the 1995 World Youth Championship after it was moved from Nigeria due to an outbreak of cholera.
French sports newspaper L'Equipe said Wednesday that Qatar might be the solution if the CAF fails to find a replacement for Morocco on the continent.
But Saud al-Muhannadi, vice president of the Qatar Football Association, on Wednesday denied the reports, which he described as "illogical."
Morocco had said since early October that its call for a postponement was due to the deadly Ebola pandemic but CAF lost patience with the North Africans and threw them out as hosts and participants with a heavy fine likely to follow.