We analyse for the first time the CP violating ratio ε′/ε in K → ππ decays in leptoquark (LQ) models. Assuming a mass gap to the electroweak (EW) scale, the main mechanism for LQs to contribute to ε′/ε is EW gauge-mixing of semi-leptonic into non-leptonic operators, which we treat in the Standard Model effective theory (SMEFT). We perform also the one-loop decoupling for scalar LQs, finding that in all models with both left-handed and right-handed LQ couplings box-diagrams generate numerically strongly enhanced EW-penguin operators Q8,8′ already at the LQ scale. We then investigate correlations of ε′/ε with rare Kaon processes ( {K}_Lto {pi}^0nu overline{nu} , {K}^{+}to {pi}^{+}nu overline{nu} , {K}_Lto {pi}^0ell overline{ell} , {K}_Sto mu overline{mu} , ΔMK and εK ) and find that even imposing only a moderate enhancement of (ε′/ε)NP = 5 × 10−4 to explain the current anomaly hinted by the Dual QCD approach and RBC-UKQCD lattice QCD calculations leads to conflicts with experimental upper bounds on rare Kaon processes. They exclude all LQ models with only a single coupling as an explanation of the ε′/ε anomaly and put strong-to-serious constraints on parameter spaces of the remaining models. Future results on {K}^{+}to {pi}^{+}nu overline{nu} from the NA62 collaboration, {K}_Lto {pi}^0nu overline{nu} from the KOTO experiment and {K}_Sto mu overline{mu} from LHCb will even stronger exhibit the difficulty of LQ models in explaining the measured ε′/ε, in case the ε′/ε anomaly will be confirmed by improved lattice QCD calculations. Hopefully also improved measurements of {K}_Lto {pi}^0ell overline{ell} decays will one day help in this context.