The daily newspaper states that the La Liga giants are pondering a January bid for the 32-year-old striker.
The report states that Barcelona are interested in the Fenerbahçe striker following rumours that Van Persie has fallen out with head coach Vitor Pereira.
Van Persie did however, start and scored the winning goal in the 1-0 victory over Kayserispor in the Turkish Super League on the weekend.
The experienced striker only joined the Yellow Canaries over the summer. Van Persie left Manchester United to sign for Fenerbahçe on a three-year deal and already has five goals to his name this season.
Barcelona will also scout Riechedy Bazoer, Davy Klaassen, Jairo Riedewald, Anwar El Ghazi and Arkadiusz Milik according to Mundo Deportivo.