The 26-year-old Sunderland striker, currently on loan at Al Ain in the United Arab Emirates, is unhappy at the "verbal abuse" that came his way during the recent CAF Africa Cup of Nations.
"Mr Gyan is frustrated over the verbal abuse he has received since playing for the country at the 2012 African Nations Cup. The GFA is in talks with Mr Gyan to urge him to reconsider his decision."
Gyan missed an early penalty, and a host of other chances, as eventual winners Zambia edged Ghana 1-0 earlier this month in the Africa Cup of Nations semi-finals.
He also missed a crucial spot-kick in the closing seconds of extra time in Ghana's 2010 FIFA World Cup™ quarter-final against Uruguay, with the South Americans going on to advance in the shoot-out.