Mata has been reduced to being a bit-part player at Manchester United and is in the final six months of his contract at Red Devils.
The Premier League giants are unlikely to offer a new deal to the Spaniard, who has made just three appearances for the club this season.
The 33-year-old is looking around for a new club in the summer and he has a few takers back at his homeland in Spain.
According to Spanish sports daily AS, Sociedad president Aperribay held talks with Mata’s father in a San Sebastien hotel this week.
It was an informal meeting and the Sociedad chief discussed the possibility of signing the midfielder on a free transfer in the summer.
Sociedad are interested in Mata and want to add a player of his stature to their squad next season.
However, the Spaniard would have to agree to a wage cut as the Spanish club cannot afford his current salary.
It remains to be seen whether the veteran Spaniard ends up at the Anoeta ahead of next season.
