Marca says Dortmund are moving for Brahim, who has just turned down a loan move to City's LaLiga partners Girona.
Indeed, the midfielder has told City management he either wants to stay with the first team or be allowed to join BVB on-loan.
The concern for City is they could lose the Spain U21 international next summer should he impress in Germany. Brahim has so far stalled on agreeing terms over a new deal with City.
The Premier League champs lost Jadon Sancho to BVB a year ago and are wary of the same happening with Brahim.