Mir, 20, has netted 15 times in 17 league appearances this season for Valencia's second team, who currently play their football in the Segunda B.
According to ElBernabeu.com, Los Blancos will pay "a small fee" to sign Mir, and the forward will initially represent Real Madrid Castilla with the view to becoming a first-team player in the future.
Mir, who represented Barcelona between 2009 and 2011, made his Valencia debut in their Champions League clash with Zenit St Petersburg in November 2015.
The forward began his career as a futsal player with CD Javali Nuevo and ElPozo Murcia FS before transitioning into full football with Ranero CF, whom he represented for two years before joining Barcelona.
Madrid are also expected to bring Athletic Bilbao goalkeeper Kepa Arrizabalaga to the Bernabeu when the January transfer window opens for business.