New head coach Thomas Christiansen and director of football Victor Orta look set overhaul Leeds' squad following the departure of Garry Monk.
Mateusz Klich has already been bought from Twente on a three-year contract last week.
The Polish central midfielder joined the club for an undisclosed fee to become Christiansen's first official Leeds signing.
Spanish newspaper El Comercio say the Whites are ready to pay up to £3m for Saiz.
But it's been reported that Huesca, who play in Spain's second tier, will only receive half the fee.
The other half will go to Saiz's former club, Atletico Madrid.
Saiz, 26, moved from the Vicente Calderon - initially on loan - in 2015.
Since making the switch he's made 48 appearances for Huesca, scoring 13 goals.
He can be deployed in a forward role or as an attacking midfielder.