The 23-year-old Ivory Coast international has been earning rave reviews in Ligue 1 so far this season for his performances, having scored five goals in eight games.
However, it’s believed that the Gunners would have to fork out around £30million for Pepe, while Barcelona and Sevilla are among those keen on his services.
According to the Mirror, as claimed by the Daily Mail, Everton are also monitoring the winger and sent scouts to watch him against Amiens where he netted a hat-trick.
Lyon tested the water last summer with a £26million offer which was rejected after Pepe hit 13 goals in 36 Ligue 1 appearances last season.
Lille struggled last season in Ligue 1, finishing in 17th position, just one place and one point above relegation.
However, its been a different story so far for the French side this season as they currently occupy second place after eight games, and Pepe’s contribution has played a big part in their turnaround in fortune.