Motivated by the recent observation of $T_{c\overline{s}0}(2900{)}^0$ and $T_{c\overline{s}0}(2900{)}^{++}$ in the $D_s\pi$ invariant mass distributions, we investigate $D^{*}{K}^{*}$ interactions in a coupled-channel approach. Within the hidden local symmetry formalism, a sizable attraction interaction is found in the $J=0$ isospin triplet sector that can form a bound or a virtual state, which is consistent with the experimentally observed $T_{c\overline{s}0}\left(2900\right)$. By reproducing a $D_s^{*}\rho \text{−}{D}^{*}{K}^{*}$ bound/virtual state with the pole mass equal to that of the $T_{c\overline{s}0}\left(2900\right)$ measured by LHCb in the sector $(I,J)=(1,0)$, we determine the unknown parameter in the loop function, and then search for possible poles in the sectors of $I=1$, $J=1$, 2 and $I=0$, $J=0$, 1, 2. The predicted resonances provide a useful reference for the future experimental studies of the $(C,S)=(1,1)$ systems and can be also helpful to unravel the nature of the $T_{c\overline{s}0}\left(2900\right)$.