The Kayserispor frontman is currently the Black Stars' all-time top scorer with 51 goals in 106 matches.
Coach Kwesi Appiah's side's current poor standing in 2018 World Cup qualifying, coupled with the 31-year-old's injury predicaments, is seemingly calling to an end a 14-year international career.
“I spoke personally to Asamoah Gyan in Kumasi and advised him to quit the national team," Sarpong, Gyan's high school coach, was quoted as saying by Ghanasoccernet.
“I have asked him to leave this team now. He has everything in football - money, houses, cars and name. Just leave this team now and save yourself.
"But he told me he wanted to qualify the team to the World Cup but now that appears difficult, he wants to qualify to the 2019 Afcon and then he will quit [after the tournament].”
Gyan made his Ghana debut in 2003, scoring in a 5-0 thrashing of Somalia.
He has since gone on to play at six Afcon tournaments, registering eight goals to his name.
He has also led the Black Stars at three World Cup competitions, but the number is unlikely to increase as the side currently sit third in Group E with two matchdays to go in Russia 2018 qualifying.
He sat out the 5-1 demolishing of Congo on Tuesday due to injury.