  In this work, we study the A$_{x}$Fe$_{2-y}$Se$_2$ (A=K, Rb) superconductors
using angle-resolved photoemission spectroscopy. In the low temperature state,
we observe an orbital-dependent renormalization for the bands near the Fermi
level in which the dxy bands are heavily renormliazed compared to the dxz/dyz
bands. Upon increasing temperature to above 150K, the system evolves into a
state in which the dxy bands have diminished spectral weight while the dxz/dyz
bands remain metallic. Combined with theoretical calculations, our observations
can be consistently understood as a temperature induced crossover from a
metallic state at low temperature to an orbital-selective Mott phase (OSMP) at
high temperatures. Furthermore, the fact that the superconducting state of
A$_{x}$Fe$_{2-y}$Se$_2$ is near the boundary of such an OSMP constraints the
system to have sufficiently strong on-site Coulomb interactions and Hund's
coupling, and hence highlight the non-trivial role of electron correlation in
this family of iron superconductors.
