In this article, we study the possible relation between the electronic and magnetic structures of the TiO₂/LaAlO₃ interface and the unexpected magnetism found in undoped TiO₂ films grown on LaAlO₃. We concentrate on the role played by structural relaxation and interfacial oxygen vacancies. LaAlO₃ has a layered structure along the (001) direction with alternating LaO and AlO₂ planes, with nominal charges of +1 and .1, respectively. As a consequence of that, an oxygen-deficient TiO₂ film with anatase structure will grow preferently on the AlO₂ surface layer. We have therefore performed ab initio calculations for superlattices with TiO₂/AlO₂ interfaces with interfacial oxygen vacancies. Our main results are that vacancies lead to a change in the valence state of neighbor Ti atoms but not necessarily to a magnetic solution and that the appearance of magnetism depends also on structural details, such as second neighbor positions. These results are obtained using both the local spin density approximation (LSDA) and LSDA + U approximations.