Michel Pont, Juan Ignacio Jimenez and Marco Tardelli are also in contention to replace Appiah after the 54-year-old left his position with the team last month.
Ghana's disappointing World Cup campaign ultimately cost Appiah his job, the African nation finishing bottom of their group with just one point from their three matches.
Former Chelsea, West Ham and Israel boss Grant arguably has the strongest record of the contenders, while Kluivert's distinguished playing career with the likes of Netherlands and Barcelona may also make up for his lack of managerial experience.
Like Grant, Tardelli has international experience having coached the Egyptian national team and his latest role saw him assist Giovanni Trapattoni with the Republic of Ireland.
Jimenez, Real Valladolid's former head coach, and Pont are also in the running when the interview process begins in mid-October.
"Pont, Kluivert and Tardelli will arrive in Accra to be interviewed on 17th October," the GFA announced. "Grant and Jimenez will be interviewed on 18th October.
"Meanwhile two coaches have been placed on standby in the event one or some of the above listed are not readily available.
"The two coaches on the standby list are Bernd Schuster and Ricardo Gareca."
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