Liverpool in recent weeks have been linked with the attacker over a Summer recoup. Klopp apparently sees the forward as an upgrade on Roberto Firmino as adding him in the squad would also give him the chance to experiment with four in the attack in slightly different formations.
But the Reds could be set to battle Premier League rivals Manchester United for his signature as they have expressed an interest in the player.
United are reportedly too targeting Pepe in a bid to replace Romelu Lukaku, who could leave Old Trafford before the start of next season.
According to multiple reports, Manchester United have now entered the race to sign Lille superstar Nicolas Pepe. With Lukaku’s future looking uncertain, United do want to bring him to the club this summer. #MUFC #LILLE pic.twitter.com/ZlBEaJDXdD
— Himmatt🇾🇪 (@FootyHimmatt7) April 29, 2019
The Belgian forward has seen his position captured by Rashford since Solskjaer's appointment and rumours have been circulating that he could move to Serie A next season, after potential interests from Inter Milan and Juventus.
United are set for a major summer shake-up under Solskjaer, with numerous first-team members expected to leave Old Trafford in the summer and Lukaku could be one of the significant big names to be sold.
With that in mind, United are actively looking for a replacement and reportedly they have been impressed with scouting reports on Pepe - who is ready to leave Lille in the summer.
However, getting the service of the forward would not appear as easy for any of the sides. With 21 goals and 11 assists in all competitions this season, Pepe has turned out to be one of the most lethal finishers in Europe attracting huge praise, having mainly hit these high figures from a wide position.
🙌 Nicolas Pépé this season 🤩
— LOSC Lille EN (@LOSC_EN) April 28, 2019
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Chelsea, Arsenal, Tottenham Hotspur are the other Premier League clubs to have been credited with an interest in the forward while other European giants Barcelona, PSG and Bayern Munich have also been linked with a move.
The attacker is likely to command a fee in the region of £60 million and his goal and assist ratio dictates that any top sides would welcome the offer.
It's still unsure where would the player ultimately move but there has been speculation that Pepe is likely to hold a media conference this week to reveal where he will play next season, with next Sunday set to be the most likely date of the announcement.