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We examine the stellar population radial gradients (age, metallicity and [$α/$Fe]) of $\sim$ 100 passive central galaxies up to $\sim 2 R_e$. The targeted groups have a halo mass range spanning from $11 < \log(M_{200}/M_{\odot}) < 15$, in the SAMI Galaxy Survey. The main goal of this work is to determine whether central galaxies have different stellar population properties when compared to similarly massive satellite galaxies. We find negative metallicity radial gradients, which become shallower with increasing stellar mass. The age and [$α$/Fe] gradients are consistent with zero or slightly positive. [$α$/Fe] gradients become more negative with increasing mass, while age gradients do not show any significant trend with mass. We do not observe a significant difference between the stellar population gradients of central and satellite galaxies, at fixed stellar mass. The mean metallicity gradients are $\overline{Δ[Z/H]/Δ\log(r/R_e)} = -0.25 \pm 0.03$ for central galaxies and $\overline{Δ[Z/H]/Δ\log(r/R_e)} = -0.30 \pm 0.01$ for satellites. The mean age and [$α$/Fe] gradients are consistent between central and satellite galaxies, within the uncertainties, with a mean value of $\overline{Δ\textrm{log (Age/Gyr)}/Δ\log(r/R_e)} = 0.13 \pm 0.03$ for centrals and $\overline{Δ\textrm{log (Age/Gyr)}/Δ\log(r/R_e)} = 0.17 \pm 0.01$ for satellite and $\overline{Δ[α/Fe]/Δ\log(r/R_e)} = 0.01 \pm 0.03$ for centrals and $\overline{Δ[α/Fe]/Δ\log(r/R_e)} = 0.08 \pm 0.01$ for satellites. This evidence suggests that the central region of central passive galaxies form in a similar fashion to satellite passive galaxies, in agreement with a two-phase formation scenario.