In the field of bioimpedance measurements, the Cole impedance model is widely used for characterizing biological tissues and biochemical materials. In this work, a nonlinear least squares fitting is applied to extract the double-dispersion Cole impedance parameters from simulated magnitude response datasets without requiring the direct impedance data or phase information. The technique is applied to extract the impedance parameters from MATLAB simulated noisy magnitude datasets showing less than 1.2 % relative error when 60 dB SNR Gaussian white noise is present. This extraction is verified experimentally using apples as the Cole impedances showing less than 3 % relative error between simulated responses (using the extracted impedance parameters) and the experimental results over the entire dataset.