Sky sources understand that the full-back told the Gunners that he had turned down their contract offer earlier this week.
Sagna's current deal is due to expire at the end of June, after which point he will be free to sign for another club. Manchester City are favourites to sign the 31-year-old.
Speaking to French sports daily L'Equipe from France's training base at Clairefontaine, Sagna said: "It's no longer a secret, I'll leave Arsenal.
"They tried to make an effort, but the discussions have not gone in the direction I wanted."
Sagna admitted he was pleased to go out on a high having been part of the side that ended Arsenal's nine-year wait for a trophy with their FA Cup win against Hull.
"To finish at Wembley with the Cup, it was something magical, " he added.
"It was an honour to evolve in that shirt, Even though we were criticised for quite some time due to the lack of trophies, I spent some magical moments there.
"If I had to do it again, I'd do the same thing."