Goal understands the centre-back has approved an annual salary of around €4.5 million, as well as a signing-on fee worth €3m, after talks between the club and player held in Madrid.
Barca have tabled an offer of €45m for Marquinhos and will go as high as €50m to land their man but PSG continue to refuse to entertain their interest.
READ MORE | Aurier doesn't deserve PSG shirt
PSG have often stated their desire to keep the ex-Roma man, who is under contract until 2019, and previously rejected a bid from Barcelona.
They face a fight to retain the 21-year-old this summer, however, given the advanced nature of the talks.
Goal understands Marquinhos' representatives are keen for their client to leave the French capital - though his agent, Giuliano Bertolucci, denied any contact with Barca when asked for comment.