The 24-year-old winger is a rising star at Ligue 1 outfit Lille.
He’s scored 35 goals in 74 games in his two years at the club.
French daily L’Équipe say Unai Emery and Jurgen Klopp have both lodged bids.
Serie A heavyweights Napoli and Inter Milan are also ready to do business.
“Nicolas Pepe is wanted by Arsenal and Liverpool”
It’s suggested Manchester United and Atletico Madrid have both registered their interest.
However, both clubs now need to offload players first.
Speculation continues to shroud Paul Pogba and Romelu Lukaku at United.
Pogba remains a top target for Zinedine Zidane at Real Madrid.
Lukaku, meanwhile, is being chased by Inter Milan.
Pogba remains the most likely departure after a challenging 12 months at Old Trafford.
The midfielder had a fractured relationship with Jose Mourinho, although gets on far better with Ole Gunnar Solskjaer.
Pogba’s agent, Mino Raiola, claimed earlier this month that his client has been keen to leave Old Trafford for a while.
“The player [Pogba] has done nothing wrong,” the Italian said.
“He has been respectful and professional in every way and always.
“The club has known his feeling for a long time.
“It is a shame other people only like to criticise without the right information, and I am also sorry that the club does not take any position against this.
“Hopefully there will be soon a satisfying solution for all parties.”
Starsport understands United now value the midfielder as high as £180m despite his eagerness to leave the club.
Spain midfielder Juan Mata says he wants Pobga to remain at the club.
“Obviously as a team-mate, and as a friend also, I would like him to stay and to be happy because he is a very good player for us,” he said.
“We know we have to do better than last season. This club has won more trophies than any other club in England.”