The 35-year-old left the club on Tuesday after being told by new boss Stuart Pearce his contract would not be renewed after three years in Nottingham.
Greening said: "I would like to thank the supporters for the backing they gave me over the course of three very enjoyable years at the City Ground.
"I will look back fondly on my time at Forest and I truly hope the club achieves its dream of promotion to the Premier League as soon as possible.
"It is my intention to continue playing for at least another season as I feel fit and capable of making a positive contribution to a team.
"I wish everyone connected with Forest the very best for the future."
Greening is followed out of the exit door by Marcus Tudgay, Guy Moussi, Matt Derbyshire, Simon Gillett, Ishmael Miller and Gonzalo Jara, who are all out of contract.