Don Balon says the striker fears his career has stalled this season after returning to Madrid and has decided he must leave.
Borja has already spoken with Real president Florentino Perez to make an informal transfer request. While Perez is unhappy with Borja's decision, he has accepted it.
A move to the Premier League has been mooted for the youngster, who spent last season on-loan with Wolfsburg.
Just last night, Borja scored twice for Spain U21 in victory over Estonia.