Second harmonic generation (SHG) has been applied to reduce background signals in near-field optical imaging, but this technique is usually limited to samples with strong second-order nonlinear susceptibilities. To overcome this limitation, in this paper, we present a versatile background-free SHG configuration, where it utilizes the second-order nonlinear susceptibility of the probe which essentially functions as a near-field polarizer capable of filtering out the background signal component. In the theoretical analysis, we first model the probe-sample optical interactions at both the fundamental frequency and the second harmonic frequency by using the coupled dipole method. The theoretical model reveals that the proposed versatile background-free SHG configuration requires two conditions. The first condition is that the incident optical field must be s-polarized. The second condition is that the probe must be made of crystals from symmetry class 222, symmetry class 622, symmetry class 422, symmetry class 42m, symmetry class 43m or symmetry class 23. To demonstrate the effectiveness of the proposed versatile background-free SHG configuration, a probe made of deuterated potassium dideuterium phosphate (DKDP) crystal from symmetry class 42m is analyzed numerically. It is shown that when imaging samples with negligible second-order nonlinear susceptibilities, the proposed background-free SHG configuration improves the imaging contrast by more than one-order of magnitude as compared to all other imaging configurations. Moreover, we also investigate the dependence of its performance on other parameters, such as the probe-sample distance, the relative size between probe and sample, and the tilt angle of probe crystal. It is believed that the proposed configuration could be widely used to achieve high contrast near-field optical imaging.