The 30-year-old forward is set to enter the final year of his contract at the end of the season, meaning that his employers are desperate to sell rather than lose him for free.
This has alerted Martinez, who is ready to snap up the experienced goal-getter.
Garcia has been in good form this term in La LIga, netting 10 times in 26 outings for the midtable side.
A product of Barcelona’s youth set-up, the versatile attacker has spent his entire career in his homeland and earned two senior international caps with Spain.
Garcia is also wanted by a number of French teams, but it is understood that he is more open to a Premier League switch.
Everton are believed to be planning for the loss of star striker Romelu Lukaku this summer, with the burly Belgian set to return to parent club Chelsea.
Another player on Martinez’s radar is Barcelona’s Isaac Cuenca.
It is thought that both he and Barca have been impressed by Gerard Deulofeu’s loan stint at Goodison Park, which may set up a temporary move for the attacker.