The 29-year-old posted on Twitter:.
Later on Tuesday, a club statement confirmed Cunningham, Michael Boxall, Josh Brindell-South, Tyler Boyd and Jason Hicks had all been released.
Cunningham will leave Phoenix with 11 goals to sit eighth on the club's all-time list.
He started 21 of 23 games in his first season but was used as an impact player this season by coach Ernie Merrick, starting in just one of his 16 appearances.
The highlight was a late double off the bench against Central Coast Mariners last month to secure a 3-2 home win.
“Everyone at the club and the supporters has been fantastic,” Cunningham said.
“I think I’ve done well in the year and a half I’ve been here and feel I can go home with my conscience saying I did my best.
“I really love the club and the people in it, but it has been difficult for the last eight months with my family being in Costa Rica after (wife) Natalia went home to have our second child.”
Phoenix coach Ernie Merrick said Cunningham’s attitude had been fantastic during his time at the club.
“Even when he was on the bench or out injured Kenny remained amazingly positive,” Merrick said.
“He was an example of how a professional footballer should behave.
“I wish him well in the future and I am sure he will be even happier playing closer to home.”
Boyd has signed a four-year deal in Portugal while Boxall has been rumoured to be on his way to South Africa - with ex-Phoenix team-mate Jeremy Brockie at SuperSport United.