The Brazilian defender has long been linked with the Catalan giants but the transfer was thrown into doubt recently after the Barcelona club completed the signing of French left-back Jeremy Mathieu from Valencia for a fee of €20m.
Spanish daily El Mundo Deportivo has reported, however, that Barcelona remain keen on signing Marquinhos from PSG, with the fee thought to be in the region of €40m.
The 20-year-old, who has one senior Brazilian cap to his name, only joined PSG last summer, completing a switch from Roma for €31.4m. He helped PSG win both Ligue 1 and the Coupe de la Ligue last season.
Barcelona are keen to add to their defence whilst the French champions are hopeful of raising money following the €50m capture of David Luiz from Chelsea.