Off contract in June, the Spain U21 starlet has so far refused City's attempts to secure him to new terms.
AS says Real have been monitoring the midfielder's situation and are keen to bring him back to Spain. Contact has aleady been made between Real and the player's family.
City signed Brahim as a junior from Malaga, but the youngster now wants to move on in search of better playing opportunities.
Real chiefs have likened him to Marco Asensio and plan to sign him next summer before potentially loaning him to a Primera Division rival for the season.