Rodriguez, 22, is in high demand following two impressive seasons on loan at Leganes.
But Europa League winners Sevilla are now understood to be on the cusp of agreeing a deal with Madrid.
The clubs are still discussing the fee, with Sevilla wanting the €20m price-tag lowered and Madrid looking to insert a 50% sell-on clause.
Sevilla coach Julen Lopetegui and sporting director Monchi see Rodriguez as an ideal replacement for Ever Banega.
Rodriguez scored 13 goals and six assists in his 64 appearances while on loan at Leganes.