Theres not much to gone on for speculation...
*Most of the Borg we've seen are Humanoid
*They have a large presence in the Delta Quadrant
Those are the only core facts that give us a possible conclusion that the Borg are inahabitants of the Milky Way Galaxy, sure, theres nothing saying that there are no "Humanoids" from outside the Milky Way Galaxy, but for the benefit of posing a theory, lets assume that the Borg come from the Delta Quadrant and were originally "Humanoid" a Species that supplemented Biology with Technology, finding the benefits, eventually things got out of hand and soon it was decided that the Species would be more efficient working as a Collective Mind, something that became Permanent and thus the Borg were Born and their desire to grow went beyond their own Race
*Most of the Borg we've seen are Humanoid
*They have a large presence in the Delta Quadrant
Those are the only core facts that give us a possible conclusion that the Borg are inahabitants of the Milky Way Galaxy, sure, theres nothing saying that there are no "Humanoids" from outside the Milky Way Galaxy, but for the benefit of posing a theory, lets assume that the Borg come from the Delta Quadrant and were originally "Humanoid" a Species that supplemented Biology with Technology, finding the benefits, eventually things got out of hand and soon it was decided that the Species would be more efficient working as a Collective Mind, something that became Permanent and thus the Borg were Born and their desire to grow went beyond their own Race