With the goal of detecting and characterizing faults and fractures in enhanced geothermal systems (EGS), a new technology involving CO2 push-pull testing, active-source geophysical imaging, and well logging has recently been proposed. This technique takes advantage of (1) the contrasting properties of supercritical CO2 and water which cause CO2 to appear distinct from surrounding brine in seismic and other geophysical logging approaches, (2) the non-wetting nature of CO2 which keeps it localized to the faults and fractures to create contrast potentially sufficient for active seismic and well-logging approaches to image faults and fracture zones at EGS sites. In this study, we evaluate the feasibility of using pressure transient monitoring during CO2 push-pull tests to complement active seismic and wireline well logging for EGS characterization. For this purpose, we developed a 2D model of a prototypical geothermal site (Desert Peak, NV) that includes a single fault. The fault zone consists of a slip plane, fault gouge, and damage zone, and is bounded by the surrounding matrix of the country rock. Through numerical simulation using iTOUGH2, we found that the pressure transient at the monitoring wells in the fault gouge shows unique traits due to the multiphase flow conditions developed by CO2 injection, and varies sensitively on the arrival of the CO2 plume and the degree of CO2 saturation. A sensitivity analysis shows the pressure transient is most sensitive to the fault gouge permeability, but also depends on multiphase flow parameters and the boundary conditions of the fault. An inversion study reveals that the fault gouge permeability can be best estimated with the pressure transient data, whereas additional CO2 saturation data do not improve the accuracy of the inversion significantly.