The 28-year-old has not played for the Black Stars since the 2014 Fifa World Cup in Brazil due to injuries.
"I know [the previous coach] Avram Grant tried to get him back. Avram went to see Kwadwo on several occasions trying to convince him to come back," Afriyie told KweseESPN.
"He has gone through some turbulent times, injuries here and there and all that. Thankfully, now he has recovered fully and is playing very well. Let's give the new coach [Kwesi Appiah] the chance to also try to get him back.
"Fortunately, he will be coming home and I will take that opportunity to talk to him and see if he is ready to come back," he added.
Asamoah, who has been capped 69 times for Ghana since making his debut in 2009, helped Juventus to lift the Italian Serie A this season, his fifth trophy.