  We investigate the $s$-wave three-body system of two neutrons and one
flavored meson with total spin-isospin $J=0,I=3/2$. The meson-neutron
scattering length can become infinitely large in an unphysical region of the
quark mass when extrapolated from strangeness to charm in the so-called zero
coupling limit. Using a low-energy cluster effective field theory, we
demonstrate that the Efimov effect is manifest in the three-body system when
the meson-neutron scattering length is extrapolated to the unitary limit of the
two-body interaction. We thereby discuss the consequence of universal physics
in the physical $K^{-}nn$ and $D^{0}nn$ systems.
