Continental football's governing body Caf has opened the door for new bids after stripping Cameroon of the hosting rights on Friday.
According to reports, Morocco and South Africa have emerged as front-runners for the nod, but Prempeh believes Ghana can equally make a statement on the back of hosting the Awcon, which ended on Saturday.
“We are hoping they [Caf] can give Ghana the opportunity to host Afcon again, we will be hosting about 24 countries," she told Class FM.
"I believe that with the Accra Sports Stadium re-touched now, we have the Cape Coast Sports Stadium, we have the Essipong [Sekondi] Stadium, which needs some renovation.
"In the Ashanti Region, we can talk of the Baba Yara Sports Stadium [in Kumasi], we can talk of the Len Clay Sports Stadium [in Obuasi]."
Ghana has already hosted the Afcon on four occasions - independently in 1963, 1978 and 2008, and jointly with Nigeria in 2000.
“Speaking of training pitches, the Paa Joe Sports Stadium [at the Kwame Nkrumah University of Science and Technology in Kumasi] can be used. We have Prempeh College [in Kumasi]. We have one at Opoku Ware [Senior High School in Kumasi]," Prempeh continued.
"In Accra, we have one at Achimota that can be worked on. El-Wak Stadium has been worked on, PRESEC Legon Park has been worked on.
“We have another stadium at Tamale - the Aliu Mahama Stadium. So, we can conveniently talk about six, seven or eight stadia that can host the tournament.
"There is no harm in trying. Even if we are given the opportunity to co-host, we would have moved from one level to another.
"I don’t see why the Normalisation Committee and, therefore, the Ministry of Youth and Sports can’t put in a try."
For the first time, the Afcon will involve 24 teams requiring at least six stadia. It will be played in June/July as against the previous January/February schedule in line with a Caf reform made in July.