Frequency response analysis is widely used for the offline diagnosis of winding deformations in power transformers. To apply it to a working transformer, the magnitude of signals of the response current, which is of the order of microamperes, needs to be measured by using Rogowski coil sensors against the load current of the order of thousands of amperes. The saturation of the power frequency magnetic field in current sensors must be inhibited to ensure the accurate measurement of response currents with such a small magnitude. The authors of this paper propose a method to suppress the power frequency magnetic field by using a sensing system involving a special connection of three-phase current sensors based on the rule that the sum of the three-phase power frequency load currents of the transformer is close to zero. Each sensor consists of two secondary-side coils: a measuring coil and an anti-saturation coil. The anti-saturation coils are connected in parallel with one anothes through small inductors to eliminate the power frequency magnetic field in the cores of the sensors. We use theoretical analysis to derive the solution to this system. The results of experiments to verify the proposed method showed that it enables the sensors to function with a transformer carrying a load current of 2333 A, while incurring a relative error in the response current that is smaller than 2%.