The Liga outfit revealed on Monday that Laporte's €65 million release clause had been paid by City as Pep Guardiola closes in on his first signing of the January transfer window.
And Goal understands the Basque club have moved quickly to fill the gap left by the French centre-back by activating Martinez's own €32m release clause.
City themselves have previously targeted a move for Martinez, 26, before eventually opting for Laporte, while Barcelona were priced out of a deal for the Spain international over the summer and instead bought Yerry Mina during the January transfer window.
Should Martinez complete his move to San Mames before Wednesday's deadline, he will become the most expensive Spanish defender in history, eclipsing the €27m that Real Madrid paid Sevilla for Sergio Ramos in 2005.
Martinez missed the majority of the opening three months of the season due to injury and as such has only made 12 Liga appearances this season, scoring once in December's win over Sevilla.
And though his arrival will help plug the gap left by Laporte domestically, he will be ineligible for Athletic's Europa League campaign having already appeared in the competition on three occasions this season.
Athletic currently sit 12th in the Liga table and face Spartak Moscow in the last 32 of the Europa League in February.