Meanwhile, the Gunners are desperate to find a replacement for the Milan-bound Mathieu Flamini and see the Cameroonian as the ideal candidate.
Makoun is not just drawing attention from north London though, with Juventus, Monaco and Marseille also said to be interested.
However, with Lille understandably keen to retain the services of the 24-year-old it would take an offer of around £11million to tempt the Ligue 1 club into a sale.
If Arsenal fail to lure Makoun to Emirates Stadium, Arsene Wenger is then likely to switch his attention to Sevilla's Seydou Keita.
The Mali international revealed at the weekend that a top four club in England has been in contact concerning a close-season transfer, but Spanish giants Barcelona are also keeping close tabs on the situation.