Adams has undergone several operations since having a heart attack after a match in September and his condition turned critical over the weekend, Ferencvaros said on their website.
Adams, 22, was taken to a Budapest hospital in September after he felt dizzy following Ferencvaros's 3-1 win over arch-rivals Ujpest.
He played six matches for the 26-times Hungarian champions this season and won eight international caps for Trinidad and Tobago.
Adams had only joined Ferencvaros in August, having previously played for W Connection, United Petrotin and Central in his homeland.
He played for his country in the under-17 World Cup in 2007, the under-20 World Cup two years later and the qualifying competition for the 2014 World Cup.
The Trinidad and Tobago Football Association had organised a fund-raising campaign in his homeland and thousands of people had bought "I support Akeem" tee-shirts.