The France fullback ends a seven-year stint with the Gunners as he opts not to extend his contract past this summer.
"It's no longer a secret, I will leave Arsenal for sure," Sagna told L'Equipe. "They tried to make an effort but the discussions have not gone in the direction I wished it. There are a lot of calls, a lot of speculation. Frankly, it gives headaches. I'll sort it all out before the start of the World Cup."
The fullback was officially approached by City the day after he helped Arsenal end its nine-year trophy drought by winning the FA Cup final.
Sagna spent seven years in North London, having joined from Auxerre in 2007.