This paper considers the problem of navigating a differentially driven nonholonomic vehicle while maintaining visibility with a (stationary) target by means of Model Predictive Control (MPC). The approach combines the convergence properties of a dipolar vector field within a constrained nonlinear MPC formulation, in which visibility and input saturation constraints are encoded via recentered barrier functions. A dipolar vector field offers by construction a global feedback motion plan to a goal configuration, yet it does not ensure that visibility is always maintained. For this reason, it is suitably combined with recentered barrier functions so that convergence to the goal and satisfaction of visibility and input constraints are both achieved. The control strategy falls into the class of dual-mode MPC schemes and its efficacy is demonstrated through simulation results in the case of a mobile robot with unicycle kinematics.