Hadronic contributions dominate the uncertainty of the standard model prediction for the anomalous magnetic moment of the muon. In this work, we describe an ongoing lattice calculation of the hadronic light-by-light contribution, performed with staggered fermions. The presence of quarks with different tastes complicates the analysis of the position-space correlation function. We present a suitable adaption of the "Mainz method". As a first numerical test, we reproduce the well-known lepton-loop contribution. Results at a single lattice spacing for the light quark contribution, using two volumes, are then discussed. Our study of the long distance behavior and finite-volume effects is supplemented by considering the contribution of the light pseudoscalar-pole. The corresponding transition form factors have been evaluated in previous simulations on the same ensembles.