The 20-year-old's contract with Valencia's second string team expires on June 30 next summer, but Real Madrid are willing to pay a small amount to ensure that they can bring him in when the transfer window reopens in January.
Valencia's general director, Mateu Alemany admitted on Thursday that he may have to negotiate a deal for the young talent next month.
He said: "With Rafa there is good understanding and we hope to find a good solution for both the player and club in the January market."
If a move does eventually come to fruition, the forward will play in Real's B team, Real Madrid Castilla.
Rafa Mir has scored 15 goals in 17 games for Valencia Mestalla in the Spanish 'Segunda División B' this season.