New physics contributions to the Z penguin are revisited in the light of the recently-reported discrepancy of the direct CP violation in K→ππ. Interference effects between the standard model and new physics contributions to
ΔS=2 observables are taken into account. Although the effects are overlooked in the literature, they make experimental bounds significantly severer. It is shown that the new physics contributions must be tuned to enhance B(KL→π0νν¯), if the discrepancy of the direct CP violation is explained with satisfying the experimental constraints. The branching ratio can be as large as 6×10−10 when the contributions are tuned at the 10% level.