The French champions could bring the 20-year-old back to his homeland as they search for midfield reinforcements
The 20-year-old has made inroads into the north London club's first-team this season, but with Arsene Wenger holding Emmanuel Frimpong in high regard, opportunities could be sparse for Coquelin, whose contract with the Gunners expires in 2013.
Other potential transfer targets for Rudi Garcia include Young Boys' 21-year-old striker Emmanuel Mayuka, Genoa's Sebastian Ribas and Brest's Nolan Roux.
Meanwhile, LOSC president Michel Seydoux has urged his team to respond swiftly after their Champions League elimination.
"We must bounce back," he told La Voix des Sports, "We must profit from this unwanted alleviation in our schedule and prove that it was an accident and not a hindrance to progression.
"We are a club where the management is prudent. We have made provisions in the budget for this situation."
Lille sit in third place in Ligue 1, five points behind leaders Montpellier.