Inspired by the experimental discoveries of $X(3872)$ ($c\overline{q}q\overline{c}$) and $T_{cc}$ ($c\overline{q}c\overline{q}$), we systematically study their orbitally excited strange partners, i.e., the $K{\overline{K}}_1$ ($q\overline{s}s\overline{q}$) system, which may be related to the recently observed ${\eta }_1(1855)$, and the $K{K}_1$ ($q\overline{s}q\overline{s}$) system. Within the framework of an accurate few-body calculation method, we employ the chiral quark model to investigate both the molecular and diquark structures of these two multiquark systems in addition to channel coupling effects. Our results show that the $K{\overline{K}}_1$ system remains a scattering state, although we have considered two different sets of parameters in our calculations to avoid the influence of parameters. On the other hand, due to the presence of a good-diquark structure in the $K{K}_1$ system, we obtain a very shallow bound state in the coupled-channel calculation, where the one-gluon, the $\eta$-meson, $f_0$-meson, and $\sigma$-meson exchanges play crucial roles. The interquark distance and component analysis also suggest that it is a loosely bound molecular state.

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