Manchester United are among a host of clubs throughout Europe who have chased the Ivorian.
United though look to have stolen a march on their rivals and agreed a deal with Pepe that could see him move to Old Trafford for five years with the option of a further year.
The current stumbling block is the standoff between Lille and the Red Devils over the 24-year-old’s transfer fee, reports Football Insider.
The Ligue 1 club value Pepe at around £70m and will look to reinvest as they prepare for their forthcoming Champions League campaign.
That is something Ole Gunnar Solskjaer doesn’t need to prepare for after the Red Devils finished a disappointing sixth.
Pepe’s 24 goals and 12 assists were a huge reason Lille managed to secure their second place finish in France, ahead of the likes of Lyon and Marseille.
United have already added one winger in Welsh youngster Daniel James.
But Solskjaer’s initial success at Old Trafford was born out of a fast-paced counter-attacking style featuring the likes of Marcus Rashford, Jesse Lingard and Anthony Martial.
Pepe would add yet another weapon to a United attack which showed in glimpses last term what it was capable of.
Seeing him arrive at Old Trafford would be a major coup for United, especially as they have been relatively quiet in the market so far.
READ MORE: Man United decide on Maguire alternative.
Solskjaer has only seen James and Aaron Wan-Bissaka arrive in Manchester for a combined £67m.
United’s main transfer target throughout the summer has been Harry Maguire, but they are Leicester are someway apart in their valuation.
The Foxes want around £80m for the 26-year-old while the Red Devils view him closer to £60m.
It has led them to seek alternatives with Napoli’s Kalidou Koulibaly one of the names mentioned and Ed Woodward has steered clear of the club’s pre-season tour as he looks to complete the desired deals.
He also had the unresolved futures of both Paul Pogba and Romelu Lukaku to contend with as the duo seek exits.