Current coach Avram Grant and the GFA have mutually agreed to go separate ways when the former's contract expires by end of the month.
The Israeli became very unpopular following Ghana's poor start to the 2018 World Cup qualifying and a rather disappointing performance at the 2017 Africa Cup of Nations in Gabon.
“Decision on the next coach of the Black Stars will be taken by the Executive Committee of the GFA on Tuesday," Afriyie told Angel FM.
"The committee will decide whether to go for a foreign coach or a local coach.
“We want to be careful when it comes to selecting the next coach of the Black Stars.
"Ghanaians want a coach who will take us to the promise land by winning the Afcon and qualifying us to the World Cup among others.”
Former France captain of Ghanaian descent Marcel Desailly has been rumoured as a potential candidate.