The 19-year-old right-back has established himself as a first-team regular with the Spanish outfit since making his professional debut in December 2020.
Indeed, Martinez has already featured 80 times for Girona across all competitions, including 42 appearances during their successful 2021-22 promotion campaign from the second tier.
Martinez has since made 16 La Liga appearances so far this season and has impressed in his first-ever top-flight campaign, showcasing his defensive nous in challenging fixtures against Real Madrid's Vinicius Junior and Barcelona's Ousmane Dembele.
The teenager's rapid rise at senior level is said to have caught the eye of a number of top European clubs including Barca and Man City.
According to Mundo Deportivo, Barcelona have identified Martinez as a potential target and they have been keeping tabs on the right-back for several months.
However, the report adds that Barca face competition from Pep Guardiola's Man City for his signature, while Atletico Madrid also hold a 'serious' interest in the right-back.
Martinez joined Barca's famous La Masia academy at the age of seven in 2010 and spent six years in the Catalan club's youth ranks before moving to La Hospitalet in 2016 and later Girona in 2018.
Barca boss Xavi saw right-back trio Dani Alves, Sergino Dest and Moussa Wague leave the club over the summer, while Hector Bellerin was brought in on a short-term deal.
Bellerin is now believed to be closing in on a loan move to Sporting Lisbon, though, which leaves Xavi with Jules Kounde, Sergio Roberto and Alejandro Balde as his options at right-back, the latter of whom naturally operates as a left-back.
Man City, meanwhile, have right-back duo Kyle Walker and 18-year-old Rico Lewis among their first-team ranks, while Joao Cancelo is on the verge of joining Bayern Munich on loan with an option to buy for around £62m.
It remains to be seen whether Barca, City and Atletico are keen to pursue a late move for Martinez before Tuesday's 11pm transfer deadline or wait until the summer.
Martinez is believed to have a €20m (£17.6m) release clause in his Girona contract, which is due to expire in the summer of 2025.