Sagna turned them down in the past because he wanted to stay loyal to the Gunners but is now ready to consider a new challenge.
The Frenchman has been on the same Arsenal contract since 2008 and is believed to be deeply upset at how he has been treated after remaining committed to the trophy-less club over the years.
In the meantime, he has seen players like Robin van Persie, Nasri, Clichy, Adebayor, Toure and Cesc Fabregas quit for more lucrative deals elsewhere.
Sagna will be a free agent in the summer and is likely to consider his options before deciding whether to commit to a new deal at Arsenal.
At 30 years old, this will be the last big contract of his career, and if Arsenal fail to win any silverware this season, it could be his last chance to move to a club capable of winning a major trophy.
The path from Arsenal to City is well trodden, with the likes of Gael Clichy, Samir Nasri, Emmanuel Adebayor and Kolo Toure swapping London for Manchester before him.
Although an offer to move to City would tempt Sagna, the prospect of moving to a large European club would also be a great opportunity, leaving Arsenal in limbo and possibly needing to search for a replacement.
It may be that on his current terms, reportedly £60,000-a-week per the Daily Star report, Sagna wants to feel that he is valued more by Arsene Wenger.
Arsenal's official Twitter account quoted Arsene Wenger as saying that he remains hopeful over a new deal for Sagna:
Having been a virtual ever-present this season, starting 19 out of 22 Premier League games as part of an Arsenal defence that has the most clean sheets in the division, per ESPN FC, he certainly makes a strong argument.
Sagna is one of the more senior players in Arsenal's team. He is reliable, consistent and one of the top performers in his position in the league.
Rather than lose him to a rival, Wenger should rethink his current offer and aim to keep Sagna for another two seasons.