Manchester United boss Ole Gunnar Solskjaer is desperate to add attacking talent to his squad after missing out on Champions League qualification.
Liverpool manager Jurgen Klopp had also considered putting a bid in for Lille winger Pepe, 24, but the player is not keen on a move to England.
According to the Sun, the £70million rated Ivory Coast international is likely to join Bundesliga champions Bayern Munich as a replacement for the outgoing Franck Ribery and Arjen Robben.
Pepe scored 22 league goals this season as he fired Lille back into the Champions League, but he is highly unlikely to play for them in the competition next season with European giants circling.
One possible outgoing deal at Old Trafford is Paul Pogba to Real Madrid who have started their summer spending spree by bringing in Eden Hazard from Chelsea.
Liverpool legend Steve Nicol has given his thoughts on Pogba’s current situation at United, and not held back in his criticism of the club.
“It’s a complete and utter shambles,” Nicol said on ESPN FC.
“Even the other players must be wondering what’s going to go on.
“[Ole Gunnar] Solskjaer’s been saying that there’s going to be mass changes.
“There’s been, as far as I’m aware, unless I’ve been under a rock somewhere, then nobody’s left, nobody’s come in, and we just don’t know.
“I don’t see how they can get rid of him without losing money for a start.
“The thing’s a shambles, you’ve got your supposed best player wanting out. What a mess.”
Another Liverpool target Domenico Berardi is far more likely to link up with Klopp at Anfield after he issued a come-and-get-me plea to the German boss.
The Sassuolo forward 24, said: If an offer arrives, be it from Milan or another club, I will evaluate it with my club.
“And if I hear that it is the right proposal, to be taken on the fly, this time I will say to Sassuolo: ‘I’ll take it’.
“Being able to choose, I would play in Liverpool. Changing remains difficult for me, but it no longer frightens me, I would do it.”