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The Black Stars will look to qualify for the play-off round when they face Ethiopia and South Africa on November 11 and 14, respectively.
Reports suggest Roma are reluctant to release the player and feel the call-up may have come too early for Afena-Gyan.
The Serie A side also is said to harbour concerns that a call-up at this stage could hamper the striker’s development.
The 18-year-old has made just two senior appearances in his fledgling career and is yet to complete the full 90 minutes of a game.
Afena-Gyan was handed his Roma debut by Jose Mourinho during last Wednesday’s Serie A win over Cagliari.
He was again given 45 minutes to prove his mettle when he came on as a second-half substitute against AC Milan at the weekend.
The teenager joined Roma only in January but has been in impressive form for the club’s U19 team, where he has scored four goals this season.
Afena-Gyan’s performances seem to have caught the attention of Mourinho, who described him as a player with special qualities.
“He [Afena-Gyan] is a player with qualities that we don’t really have in the squad. He’s a player who looks for opportunities that we don’t often try to exploit,” the Roma boss said, as quoted by Goal.
“We have a lot of players who want the ball at the feet; we don’t have many who look for the spaces to run into. I like him because of how he tries to run into space and how he works out on the pitch. How he presses. He’s aggressive in the spaces.
“He is a long, long way from being the finished product - a long way from being a complete player and a long way from being the perfect player to start for a team like Roma. But he is a player that deserves to be worked with and deserves a chance to play.”
Meanwhile, Ghana coach Milovan Rajevac will name his squad for the World Cup qualifiers against Ethiopia and South Africa on Thursday afternoon.