The centre-back has caught the attention of the Catalans, who are said to be keen to strengthen in defence in light of Carles Puyol's injury problems and Gerard Pique's dip in form
The defender, who turns 21 on Thursday, is considered one of the brightest young talents in Spain and it has been claimed that the Blaugrana are mulling over a summer swoop for the Basque.
However, Martinez has declared himself happy at the Anoeta and explained that his sole concern at the moment is on getting himself back to full match fitness after his recent knee injury.
"I do not think anything of it," the centre-back said of Barcelona's alleged interest on his club's official website.
"Every year everyone does the best they can but I am comfortable here and I have many years ahead of me with Real.
"I have probably come back too quickly [from injury] and am struggling to pick up the pace, so the important thing for me now is just to get well for next season."
Martinez, who has been capped four times by the Spain Under-21s, came through Sociedad's youth system and spent two years with the B team before being added to the senior squad last season.