The Gunners have started tracking the 23-year-old after a strong start to the season.
And, according to Le 10 Sport, they have made contact with both Lille and the player to let them know he is on their radar.
It is claimed they have even told him if he continues his current form they will launch a bid either in January or the summer.
Pepe, 23, has three goals in eight caps for Ivory Coast and has impressed for Lille since breaking into the first team last season.
He joined from Angers in 2017, signing a five-year deal and has one goal and three assists so far this season with Lille fourth in the table.
Pepe plays up front or out wide and would add to the options at the Emirates after a difficult start under Unai Emery.
Arsenal have lost two of their first four games – to Manchester City and Chelsea – but are back on track after wins over West Ham and Cardiff.
They face Newcastle today and sit in ninth place. Emery is keen to build on the progress being made and believes they are heading in the right direction.
“Firstly we need to win and I think it is very important that in the last match we won,” he said on Thursday.
“Our aim away at Newcastle on Saturday is to keep improving things and continue to create our idea, build up our spirit on the pitch, individually and collectively, and it is clear this process is one process.
“Saturday is another step we can do, it will be difficult but I want to continue [to show] our personality on the pitch and impose this personality on the opposition and to find the win.”
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