The Camp Nou outfit find themselves in a position to spend big after offloading Neymar to Paris Saint-Germain for a record-breaking €222 million transfer fee.
Part of that windfall is set to be invested in Spain international Martinez, with Sociedad confirming that interest in the 26-year-old has been shown.
Sporting director Loren Juarros told reporters on Friday: "It's true Barca have spoken with us.
"They've been in contact to show their interest in the player. But so far there is no offer on the table. That's all we can say.
"La Real have no intention of facilitating Inigo's exit to any club. He is irreplaceable. We do not want to sell him."
With Sociedad reluctant to sell, Barca will need to trigger Martinez’s reported €32m buy-out clause in order to push an agreement through.
Goal understands that those in Catalonia are willing to meet that figure.
Martinez will bolster a centre-half unit at Camp Nou which already includes Gerard Pique, Samuel Umtiti and Javier Mascherano.
It is expected that another addition to the ranks will see Thomas Vermaelen moved on.
Any deal for Martinez will also see Barca complete their third capture of the summer, following deals to bring Gerard Deulofeu back to the club and to acquire Nelson Semedo from Benfica.