The 26-year-old is a target for West Ham too but David Moyes fears the former U21 global prefers a move to over staying in.
Coquelin, 26, is under contract with Arsenal for another three years.
"I can talk about the players who are here and if anyone joins us [this month] I will happily talk about him in due course. It's very hard to talk about those who aren't".
When asked if Coquelin had gone following the Gunners goalless Carabao Cup clash with Chelsea, Wenger simply replied: "Yes".
Elneny, 25, has fallen out of favour at north London this term, playing just 5 Premier League games as manager Arsene Wenger has preferred the pairing of Granit Xhaka and Aaron Ramsey. Signing Coquelin would strengthen their midfield options in the second half of the season. Only Geoffrey Kondogbia arrived, but Marcelino has maintained interest in the Arsenal player. Reports in the last 24 hours suggest that the price would be between €12-14 million.