Red Devils boss Ole Gunnar Solskjaer is preparing for a huge squad overhaul this summer and has highlighted attack as an area to strengthen.
According to the Express, United have sent scouts to watch Pepe in France and have been impressed with his performances for the Ligue 1 side.
The 23-year-old, who is understood to be seeking pastures new this summer, has notched 20 goals this season.
Liverpool have reportedly already made contact with Lille over wide man Pepe in an attempt to pip their Premier League rivals to his signature.
The hit-man was a target for Barcelona at the start of the season and a number of English clubs are now said to have shown an interest.