Within an extended chiral constituent quark formalism, we investigate contributions from all possible five-quark components in the octet baryons to the pion-baryon ($sigma_{pi B}$) and strangeness-baryon ($sigma_{s B}$) sigma terms; $B equiv N,~Lambda,~Sigma,~Xi$. The probabilities of the quark-antiquark components in the ground-state baryon octet wave functions are calculated by taking the baryons to be admixtures of three- and five-quark components, with the relevant transitions handled {it via} the $^{3}$P$_{0}$ mechanism. Predictions for $sigma_{pi B}$ and $sigma_{s B}$ obtained by using input parameters taken from the literature are reported. Our results turn out to be, in general, consistent with the findings via lattice QCD and chiral perturbation theory.