  We consider the general D=4 (10+10)-dimensional kappa-deformed quantum phase
space as given by Heisenberg double \mathcal{H} of D=4 kappa-deformed
Poincare-Hopf algebra H. The standard (4+4) -dimensional kappa - deformed
covariant quantum phase space spanned by kappa - deformed Minkowski coordinates
and commuting momenta generators ({x}_{\mu },{p}_{\mu }) is obtained as the
subalgebra of \mathcal{H}. We study further the property that Heisenberg double
defines particular quantum spaces with Hopf algebroid structure. We calculate
by using purely algebraic methods the explicite Hopf algebroid structure of
standard kappa - deformed quantum covariant phase space in Majid-Ruegg
bicrossproduct basis. The coproducts for Hopf algebroids are not unique,
determined modulo the coproduct gauge freedom. Finally we consider the
interpretation of the algebraic description of quantum phase spaces as Hopf
algebroids.
