The Whites appear to be prioritising signing a new stopper this month, with Bailey Peacock-Farrell's form being questioned at various points throughout the campaign and summer signing Jamal Blackman already returning to Chelsea due to injury.
The Daily Mail reports that Casilla is close to moving to Elland Road, but Marcelo Bielsa is keeping his options open and Martinez is said to be one of several targets apparently on their radar should the 32-year-old's move fall through.
Martinez - who earns £10,000-a-week at the Emirates, according to Spotrac - is more than capable of playing out from the back, so it is no surprise that he is a player that could be considered should they fail to sign their reported number one target.
Peacock-Farrell has generally enjoyed a good season. But there have been moments that have left the supporters concerned about whether he is ready to be the clear number one at this stage of his career.
Casilla looks as though he could be a fantastic addition. But it is clearly smart from the Championship leaders to keep other options in mind in case the move does not go through.