The 24-year-old French midfielder was ruled out for at least two months after suffering a knee injury against West Brom on Saturday.
Coquelin has been one of the key players for Arsenal this season, and his loss is a huge blow for the Gunners. His absence will force Arsene Wenger to search for a replacement as soon as the window re-opens in January.
Lucas Biglia has been a long term target of Arsenal, but according to Gazzetta World, the Gunners are unlikely to make a move for the Lazio midfielder.
The Argentine midfielder has been an epitome of consistency for Lazio since joining the Italian club in 2013.