The two players are doubtful for the final matchday encounter in Cape Coast after pulling out of training on Wednesday.
According to the Ghana Football Association, Gyan has suffered "what looked like a thigh injury" and will, therefore, undergo further tests in Accra on Thursday.
Should he fail to be passed fit for the match, it will be the fourth successive time the former Sunderland frontman is forced out of a Ghana match after sitting out the last three games against Congo, Uganda and Saudi Arabia.
A considerable layoff will also be a major blow to Turkish club side Kayserispor, who have been involved in a fitness battle over the forward since signing him in July.
Newcastle United attacker Atsu also failed to complete Wednesday's session as an injury picked up on club duty continues to take a toll.
According to the GFA, the former Porto man "withdrew with a thigh complaint", and will continue to be "assessed by doctors ahead of Sunday's game".
While playing against Bournemouth in the English Premier League on Saturday, the winger tweaked a muscle after attempting a shot, leading to his withdrawal moments later.
It was initially feared that the winger may not honour Ghana's invitation as Newcastle boss Rafael Benitez confirmed the 25-year-old's possible injury relapse during his post-match interview.