The 26-year-old forward has a hamstring injury which threatens his participation in the tournament this month.
A decision on the possibility of a full recovery, by the time Ghana play their first match on January 24, must be be made by midnight, the deadline for the submission of squads to the Confederation of African Football's headquarters in Cairo.
"Asamoah will only be taken to the competition if he recovers on time," the Ghana Football Association president Kwesi Nyantakyi told the Ghana News Agency on Wednesday.
The former Sunderland striker, now on loan in the United Arab Emirates, has been working with a Serbian medical team put together by coach Goran Stevanovic since arriving at Ghana's pre-tournament training camp in Rustenburg, South Africa earlier this week.
"I'm really important to the team and I will do anything possible to get fit for the Nations Cup," Gyan told the Ghana Football Association website last week.
Ghana have high hopes of winning he title after finishing runners-up at the 2010 tournament and reaching the World Cup quarter-finals 18 months ago. They play in Group D at the Nations Cup with Botswana, Guinea and Mali.
Tunisia are also waiting until just before the deadline to submit their squad because of injuries to Issam Jemaa and Mejdi Traoui.
AJ Auxerre striker Jemaa returned to light training in Dubai, where Tunisia are based this week, on Tuesday but Traoui is still sidelined, officials said.
Tunisia are in Group C with co-hosts Gabon, Morocco and Niger.
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