Abstract By employing an expansion in terms of the inverse multipole number, we derive analytic expressions for the quasinormal modes of scalar, Dirac, and Maxwell perturbations in the Hayward black hole background. The metric has three interpretations: as a model for a radiating black hole, as a quantum-corrected black hole owing to the running gravitational coupling in the Asymptotically Safe Gravity, and as a black hole solution in the Effective Field Theory. We demonstrate that the obtained compact analytical formulas approximate quasinormal modes with remarkable accuracy for $\ell > 0$.