  We compute some normalized structure constants in the $\eta$-deformed
$AdS_5\times S^5$ in the framework of the semiclassical approach. This is done
for the cases when the "heavy" string states are finite-size giant magnons
carrying one angular momentum and for three different choices of the "light"
state: primary scalar operators, dilaton operator with nonzero momentum,
singlet scalar operators on higher string levels. Since the dual field theory
is still unknown, the results obtained here must be considered as conjectures
or as predictions from the string theory side.
  Keywords: Gauge/string duality, Correlation functions
  PACS:11.25.-w, 11.25.Tq
