The Gunners are concerned the French international will walk away for nothing at the end of the season when his contract expires.
Wenger is keen to open talks over a new deal with the 30-year-old, but it is looking increasingly likely Sagna will choose to leave the Emirates.
Sagna is aware that his age means he will probably get one last major contract, and knows that walking away for free will increase the likelihood of being offered a larger wage packet elsewhere.
He is currently earning around £60,000 a week on the contract he signed upon his arrival in 2007.
He has reportedly turned down more lucrative offers in the past from the likes of Manchester City and Real Madrid, but is understood to have privately acknowledged this will be his final season in England.
Sagna was said to be angry at the fact Arsenal had previously only offered him a one year extension on the same money, after his years of service to the club.
He looked set to quit the club in the summer, until he was convinced to stay for another season.
His performances this season have prompted Arsenal to renew their attempts to keep him, but unless a substantial improvement to his wages are made, then the defender is likely to walk away at the end of the season.