Mundo Deportivo says Bardghji's agent was in Barcelona on Thursday and had lunch with Barca directors, including sports chief Deco.
The LaLiga champions are said to be oscillating between two options: either bringing in Bardghji as a free agent in January, or paying €2-3m to sign him immediately. Bardghji's deal with FCK expires at the end of 2025.
The latter option would mean securing the player rather than risking him going to a rival.
Bardghji is said to be "eager to sign" and that Barca "would have no problem reaching an agreement with him".
Olympique Marseille have reportedly ruled out a deal due to doubts over his fitness. Bardghji suffered a cruciate ligament injury in May last year.
However, Mundo Deportivo reports Barcelona have confirmed via medical reports that he has fully recovered and are therefore pressing for a transfer.