Los Rojiblancos met with Girona’s sporting director Quique Carcel weeks ago to notify their interest in Martinez, who has been one of the revelations in La Liga this season.
It has also led to interest from European heavyweights, including Barcelona and Manchester City.
Atletico have had their opening bid turned down by Girona, but they have obtained the right to the first refusal for the 19-year-old, which gives them the edge over other interested parties.
Girona has placed a release clause worth €20 million for Martinez. A January transfer looks less probable, but Atletico are confident about his transfer next summer.
Los Rojiblancos are looking to solidify their right-back position, with Nahuel Molina the only reliable option in that slot.
Although Marcos Llorente is a capable full-back, he has primarily been used in the midfield and attacking positions this season to a higher degree of success.
Martinez has been tipped as the future of the Spanish national team, and he could also be a great investment for Atletico’s long-term plans.
Fellow rivals Barcelona are also as keen as Atletico in the pursuit of Martinez, as the right-back slot remains an area of concern for the Catalan giants.
The Spanish U21 international also spent a significant part of his youth career at La Masia, and he also recently expressed his desire to return to Barca.
Atletico have been one of the busiest clubs in the January transfer window, selling both Matheus Cunha and Joao Felix while signing Memphis Depay from Barca.
More departures are expected to follow, with Bayer Leverkusen in talks to sign Felipe, while Saul Niguez has been linked with a move to Valencia.
If the two players were to leave, Atletico could try to sign Leicester City centre-back Caglar Soyuncu.
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