According to him, both footballers are natural leaders and have what it takes to control players in the dressing room.
Appiah also named Michael Essien as another player who could succeed in coaching, but said the midfielder’s reserved persona could be problematic.
"I think Asamoah Gyan has the qualities, Andre [Ayew] has the quality of motivating players and so if he becomes a coach one day I won't be surprised,” he told Otec FM, as quoted by Ghanasoccernet.com.
“Someone like Essien, he can be a good coach but his only problem will be to learn how to get close to his players because he is someone who is very reserved."
Appiah was, however, quick to add that not every great footballer ends up becoming a good manager.
In his view, come footballers reject the opportunity to become coaches due to the pressure that comes with the job.
"Not every player wants the coaching job because most of these players feel there is a lot of pressure in being coach,” he opined.
"But players who become coaches are players who are leaders on the pitch. They know how to control their players and motivate them on the pitch.”
Appiah was reappointed as Black Stars coach in 2017, taking over from Israeli manager Avram Grant.
However, his tenure came to an end on December 31, 2019 after the GFA declined the chance to have it renewed.