The French international is out of contract in the summer and is currently free to talk to other clubs.
Arsenal boss Arsene Wenger is confident that Sagna will commit his future to the club, however the defender is believed to have turned down two contract offers already.
The hold-up appears to be centre around the length of the deal. Arsenal first offered Sagna a one-year extension before putting forward a new deal over two years.
However the 31-year-old is reportedly holding out for a three-year contract, and wants a wage increase from his current salary of £70,000-per-week to earn £100,000. That works out at around £15.6 million over the length of the three-year deal.
According to the Telegraph, Sagna has four-year offers on the table form clubs in Turkey in France should he not receive the desired offer from Arsenal.
The newspaper adds that Arsenal are preparing contingency plans for if Sagna does leave the club in the summer, and are drawing up a list of replacements.
Sagna joined the Gunners from Auxerre back in 2007 and has since made 269 appearances for the club.
Meanwhile, The Telegraph also report that Aaron Ramsey is aiming to make his comeback from injury against rivals Tottenham next month.