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.
