The local environment of Mn atoms in (ZnO(30) angstrom/Mn(t))(n) multilayers (ML) has been studied by means of x-ray absorption spectroscopy at the Mn K edge. A series of ML has been prepared by sputtering with approximately constant total amount of Mn (300 angstrom) while the Mn layer thickness (t) has been varied from 60 to 1 angstrom (modifying consequently the number of Mn-ZnO interfaces) in order to study the Mn-Zn-O system. Variation of the Mn layer thickness (t) has been directly associated with changes in the Mn oxidation states within the sample series. Absorption spectroscopy results for films with t <= 15 angstrom indicate mostly MnO(2) formation and no signal of Mn in the ZnO lattice is found. Conversely, films with t >= 30 angstrom present two different Mn environments, that have been related to the coexistence of rocksalt and wurtzite phases, formed by Zn(1-x)Mn(x)O mixed solid solutions. The magnetic behaviour of samples is correlated with structural properties. That correlation strongly points towards substitutional Mn in the wurtzite phase as the origin of the observed ferromagnetism above room temperature.