Self-interactions between dark matter particles can induce core formation in galaxies and lead to thermalization of their central regions. The strength of self-interactions between dark matter particles is correlated to the size of the thermalized regions. The possibility of placing a conservative limit on the self-interaction cross-section by analyzing the distribution of core radius in isolated galactic haloes is explored in this work. We systematically use dark matter only $N$-body simulations of spherically symmetric isolated haloes incorporating isotropic self-scattering. We report a conservative upper limit on the self-interaction cross-section, $ \sigma/m < $ $ 9.8 $ $\ \rm cm^2 /\rm gm $ at $ 95 \% $ confidence level by comparing the generated distributions with the observed data.