Goal revealed last week that the Camp Nou club were close to reaching an agreement for the 26-year-old centre-half, as they prepared to part with some of the money generated by the sale of Neymar to Paris Saint-Germain.
Barca were seemingly prepared to meet the €32 million release clause in Martinez’s contract and get a deal done, with Sociedad director Loren Juarros admitting to talks.
He said: "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."
It is Sociedad’s reluctance to sell which is now proving to be a stumbling block, with Barca reluctant to pay the full fee in Martinez’s contract.
Instead, they are hoping to reach a compromise which will see €25m change hands and Rafinha head to San Sebastian on loan.
Barca are eager for the Brazilian to play first-team football following a serious injury last season and believe a spell with Sociedad could be beneficial to all concerned.
No deal has been agreed, though, and Martinez has no intention of forcing the issue.
As a home-grown product, he will remain loyal to his current employers and make himself available whenever he is required – with it possible that he could figure in a friendly in Burgos on Wednesday after sitting out Saturday's clash with Watford.