The 33-year-old forward joined the club in January on a six-month deal after leaving Al Sadd towards the end of last year.
During his time at Nottingham Forest, Ayew made 13 appearances under the guidance of manager Steve Cooper.
The club had signed him to bolster their squad with experience and enhance their chances of avoiding relegation from the Premier League.
Despite his efforts, Ayew was unable to find the back of the net during his 306 minutes of action for the team. Additionally, he had a missed penalty during his time on the pitch.
With his contract now expired, the Ghanaian striker is currently a free agent. He is now focused on finding a new club ahead of the upcoming season.