  Let $\mathcal{A}$ and $\mathcal{B}$\ are $C^{{\huge \ast}}%
$-algebras\textbf{.} A\textbf{ }linear map $\phi:\mathcal{A\rightarrow B}$ is
$C^{\ast}$-Jordan homomorphism if it is a Jordan homomorphism which preserves
the adjoint operation. In this note we show that $C^{\ast}$-Jordan
homomorphisms -- under mild assumptions -- preserving covariance set and
covariance coset in $C^{\ast}$-algebras.
