We present the construction of the Dirac sigma models by gauging the 2-dimensional nonlinear sigma models, but also including the possibility of nonminimal coupling to the metric sector. We show that for a large variety of possible cases, the minimal coupling to the metric sector is the only nontrivial possibility. In addition, we present the construction of the classical Batalin-Vilkovisky action for the Dirac sigma models. We follow a direct approach in its construction, by requiring it to be a solution of the classical master equation.