We consider Palatini f(R, T) gravity models, similar to those introduced by Harko et al. (2012), where the gravitational Lagrangian is given by an arbitrary function of the curvature scalar R and of the trace of the energy-momentum tensor T. Interior spherical static solutions are studied considering the model of matter given by a perfect fluid configuration and a polytropic equation of state. We analyze the curvature singularities found previously for Palatini f(R) gravity and discuss the possibility to remove them in some particular f(R, T) models. We show that it is possible to construct a restricted family of models for which these singularities are not present.