In his three appearances for Madrid’s second team, Reinier scored two goals and assisted one.
And a move to Bayer could provide him with vital experience in a league noted for its player development.
But Leverkusen are poised to win the race with a deal thought to be close.
It could provide the German club with a low-cost replacement for Kai Havertz if he moves to Chelsea.
Chelsea are in talks with Leverkusen for Havertz and he already has a personal agreement with the English club.
However, the clubs still have to agree a fee with Bayer holding out for €100m.