The origin of an extraordinary X-ray burst (XRB) associated with a fast radio burst (FRB) such as FRB 20200428 is still unclear, though several models, such as the emission of a trapped fireball modified by resonant cyclotron scattering, the outflow from a polar trapped-expanding fireball, and the synchrotron radiation of a far-away relativistic shock, have been proposed. To determine which model is true, we study the possible X-ray polarization signature for each model, inspired by the importance of radio polarization in identifying the FRB origin. We first numerically simulate or calculate the XRB spectrum for each model and fit it to the observed data, then compute the corresponding polarization signal based on the fit. We find that these three models predict different polarization patterns in terms of phase/time and energy variations. The differences can be used to test the models with future X-ray polarization observations.