The translational and orientational dynamics of a spheroid suspended in a viscoelastic liquid flowing in a wide-slit microchannel is studied by 3D finite element simulations. An Arbitrary Lagrangian-Eulerian formulation is adopted to handle particle motion. The particle dynamics, with specific interest on the migration phenomenon and on the long-time orientation, is studied by computing the trajectories of the spheroid and the orbits described by its orientation vector. The effects of the initial distance from the channel centerplane and of the initial orientation on the particle motion is investigated, for low and moderate Weissenberg numbers. A ‘migration state diagram’ giving the long-time equilibrium positions of the particle for all possible initial configurations is derived: in most cases, the particle goes to the centerplane, but there are circumstances where also the wall is an attractor.