Rare K rightarrow pi nu bar{nu } decays, being dominated by short distance contributions within the standard model (SM), open a window for new physics (NP) searches at low energies. The K rightarrow pi nu bar{nu } branching ratios are expected to be measured with sim 10% accuracies by NA62/CERN and KOTO/JPARC. The theoretical uncertainties of branching ratios within the SM are well under control. In the B sector, it is tentative to explain the B-meson anomalies R_{D^{(*)}} and/or R_{K^{(*)}} by effects of physics beyond the SM. Although NP seems to be present in the third fermion generation it might also manifest in the flavor changing neutral current transition s rightarrow d . Together with the anticipated good experimental sensitivities and accurate theoretical predictions for Krightarrow pi nu bar{nu }, this motivates studies of correlated effects of NP in rare Krightarrow pi nu bar{nu } and B rightarrow K^{(*)} mu ^+ mu ^- decays. Here we consider the loop induced effects in K rightarrow pi nu bar{nu } in two leptoquark models designed to address lepton-flavor universality violation in the R_{K^{(*)}} anomalies.