Martín, 20, was one of the standout performers in the Copa del Rey final, playing the full 120 minutes as Real Sociedad defeated Atlético de Madrid on penalties last weekend.
That display dramatically accelerated his profile among Europe's top clubs, reports AS.
Real Sociedad have made their position clear: they will not negotiate and will only release Martín if the full €50 million release clause is triggered. His contract runs until 2031.
The meeting between Deco and agent Iñaki Ibáñez is described as exploratory rather than concrete. Barcelona have not communicated any formal intention to sign Martín to the player directly.
Bastoni remains the priority. However, his deal has not yet received the green light from Flick, who has yet to confirm to the club's hierarchy that the Italian fits his system.
Real Madrid have also been monitoring Martín throughout the season, making this a potential straight fight between the two Spanish giants if Bastoni's move collapses.