The centre-back made 239 appearances for Real Sociedad before he completed a switch to Basque rivals Athletic Bilbao in 2018.
In five years with Los Leones, Martinez has featured on 169 occasions, chipping in with seven goals and seven assists.
Although he has established himself as a key figure in Athletic Bilbao's side, he was linked with a move to Barcelona in the summer.
Ultimately, no transfer materialised as the Catalan giants decided to strengthen their defence with the additions of Jules Kounde and Andreas Christensen.
However, Barcelona are still keen to add to their defensive ranks after Gerard Pique called time on his career as a professional footballer in November.
Martinez is still a target for Xavi's side, and according to Sport, they are closing in on a deal to sign the 31-year-old next summer.
Barcelona are confident that they can reach an agreement to sign the experienced defender on a free transfer when his current contract expires in June.
There has allegedly been no formal offer from the Basque club, although Athletic Bilbao's sporting director Mikel Gonzalez has previously indicated that they would be keen to retain Martinez's services.
While the player is happy to remain at San Mames until the end of the season, there is a belief that he favours a move to Camp Nou.
Barcelona appears to be at the front of the queue, Martinez has received a number of offers from other interested clubs, while Atletico Madrid are reportedly believed to be among his admirers.
While Martinez could be on his way to Camp Nou in the summer, a recent report suggested that Barcelona could allow a couple of players to leave at the end of the current campaign.
Hector Bellerin, who joined on loan from Arsenal in September, and Memphis Depay could both be let go on free transfers, while January departures for the pair have not been ruled out.
Meanwhile, veteran midfielder Sergio Busquets is also out of contract at the end of the season, but he is currently considering his future as he nears 700 Barcelona appearances.