  We have considered the penguin interaction contribution to $K \rightarrow 2
\pi$ decays. In particular, we have investigated the effect of the momentum
dependence of the penguin coefficient. Our analysis is performed within the
Chiral Quark Model where quarks are coupled to the pseudoscalar mesons, which
means that hadronic matrix elements can be calculated in terms of quark loop
diagrams. We have inserted the momentum dependent penguin coefficient into the
relevant quark loop diagrams for $K \rightarrow \pi$. We discuss two possible
prescriptions for performing the calculations, and conclude that the momentum
dependence of the penguin coefficient increases the amplitude by 10-20 $\%$. In
any case, the (CP-conserving) penguin contribution is very sensitive to the
values chosen for the involved parameters.
