The France international full-back's contract situation became a long-running saga during last season, with boss Arsene Wenger asked about it on a weekly basis.
The 31-year-old has yet to accept the offer put before him and has now appears to have said he will not be doing.
"It's no longer a secret, I will leave Arsenal for sure," he told L'Equipe.
"They (Arsenal) tried to make an effort but the discussions have not gone as I wished."
The former Auxerre man's final game in an Arsenal shirt now looks set to have been the FA Cup Final win over Hull two weeks ago.
"There is no ideal end but it was a dream to finish like that, at Wembley, with the cup," he added.
"It was an honour to wear the shirt."
Sagna refused to comment on who his next club would be but added "I'll fix that before the start of the World Cup".
"I don't know where to start or even how to say it but I just wanna thank Arsenal FC, a family to me, a club who taught me so much in 7 years," he said on his Twitter feed.
"Now it's time for me to move on and one more time THANK YOU."
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- Arsene Wenger