The Frenchman has snubbed the London club's final offer and will now look to move to the likes of Manchester City, Chelsea or PSG in search of a raise.
The Frenchman let manager Arsene Wenger know at the end of last week that the FA Cup final against Hull City on Saturday will be his final game for the club.
Arsenal had been close to an agreement with Sagna last month after offering him an 100,000-euro-a-week, two-year deal — with the option of a third year — in a final attempt to keep him at the club.
However, the 31-year-old has rejected the offer and later this month will open talks with suitors, who include Manchester City, Chelsea, Liverpool and Ligue 1 champion Paris Saint-Germain.
City and Chelsea are believed to be ready to hand Sagna the 120,000-euro-a-week deal he is after.
The Gunners hierarchy was unwilling to stretch beyond 100,000 euros a week for a fullback in his 30s and Sagna will end his seven-year spell with Arsenal after Saturday's final at Wembley.
The right back is believed to be settled with his family in London, but will hold negotiations with a number of Premier League rivals, as well as clubs elsewhere in Europe, before making a decision on his future.
Losing Sagna will be a blow to Arsene Wenger, with the player offering experience and versatility that is not easy to replace. He filled in at center back against Norwich City on Saturday as Wenger chose to rest Per Mertesacker ahead of the cup final.
Speaking recently of Sagna, Wenger said: "We know what we want from him, he knows what is on the table and that's where we are. The ball is not in our camp any more. It is in his camp and he needs to come back to us."
The Gunners have looked closely at replacement right backs in the last year, with Frankfurt's Sebastian Jung and Toulouse's Serge Aurier currently on top of their target list to replace Sagna.
The defender, who turned 31 in February, is able to join another club on a free transfer July 1.