The parties are expected to close the agreement in the coming weeks. The Mexican is said to be on very good terms with Joan Laporta.
42-year-old Marquez was a sporting director of Mexican side Atlas between 2018 and 2019. Juvenil A could be his first coaching experience in Marquez's career.
Rafa Marquez was part of Blaugrana between 2003 and 2010, winning 11 trophies with the club, including 2 Champions League cups.
Laporta breaks silence on ongoing contract negotiations with Messi
"Will Messi renew? You have to ask him. I'll do what I can within the club's possibilities. We are trying and I see Leo as very motivated, as well as a fantastic person who wants to continue at Barca, I'm convinced," Laporta added.
Messi's contract extension saga have stalled for some time leading to rumours linking him away from Barca.
Last year, Messi requested to be sold following irreconcilable differences with the club administration then.
Things are better now and Laporta is confident he can get the Barca captain to extend his current deal.
Laporta invites former rivals Victor Font and Toni Freixa to Copa Del Rey final, Bartomeu too
Joan Laporta has invited Victor Font and Toni Freixa to Barca's Copa Del Rey clash against Athletic Bilbao on Saturday, according to RAC1.
Former caretaker president Carles Tusquets has also been invited to the game. Embattled former president Josep Maria Bartomeu was also invited but he reportedly declined.
Barcelona are the most successful team in Copa Del Rey history with 30 triumphs. The Blaugrana will be looking to rubberstamp their dominance in the competition against the Lions this weekend.