The Real Sociedad centre-back has emerged as one of Spanish football's most highly regarded young defenders, having established himself in the first team last season and continued to build on that form at the start of this campaign.
According to Fussball News, Arsenal, Chelsea and Liverpool are all monitoring the 20-year-old's development closely, with the north London club having tracked him for some time.
Real Madrid and Barcelona have also been credited with long-standing interest. Real Madrid's own need for a new centre-back is understood to have put the Basque defender on their radar for a future window.
Martín has already forced his way into Spain's Under-21 squad on a regular basis and won his first senior cap earlier this year, featuring for the national team in a pre-World Cup friendly against Iraq before missing out on Luis de la Fuente's final squad for the tournament itself.
His rise has pushed his value up sharply. A new contract signed with Real Sociedad a few months ago runs until June 2032 and carries a release clause of €60 million (£52m).
Real Sociedad could explore a structure involving a lower fixed fee - in the region of €50 million, plus variables that would approach the full release clause - along with a percentage of any future sale, should they eventually be forced into negotiating his departure.
For now, Real Sociedad's stance remains that any suitor would need to meet the clause in full rather than negotiate a discount, reflecting the club's determination to hold on to one of the most promising products to emerge from their Zubieta academy in recent years.
The defender has shown few signs of being distracted by the speculation, remaining a regular fixture in Real Sociedad's back line while combining physical strength in duels with a composure on the ball that has attracted admirers beyond Spain.
With interest also stretching to the Premier League, what began as a domestic story involving Spain's two traditional giants has widened into a genuine multi-league pursuit for Martín's signature.