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In this work we calculate the decay widths of $\phi(2170)$ to $\phi\eta$ and$\phi\eta^\prime$ by considering $\phi(2170)$ as a $\phi K\bar K$ state, with$K\bar K$ clustering as $f_0(980)$. These decay widths have been recentlydetermined by the BESIII, BaBar and Belle collaborations with the aim ofunraveling the nature of $\phi(2170)$. By analyzing the data on the crosssections of the process $e^+e^-\to\phi\eta$, two solutions were found by theBESIII collaboration with the same $\chi^2/n.d.f$, mass and width for$\phi(2170)$. However, different values for$\mathcal{B}^{\phi(2170)}_{\phi\eta}\Gamma^{\phi(2170)}_{e^+e^-}$ wereobtained: $0.24^{+0.12}_{-0.07}$ eV (solution I) and $10.11^{+3.87}_{-3.13}$ eV(solution II). In case of$\mathcal{B}^{\phi(2170)}_{\phi\eta^\prime}\Gamma^{\phi(2170)}_{e^+e^-}$, avalue of $7.1\pm 0.7\pm 0.7$ was determined by the BESIII collaboration fromfits to the data on the cross section of $e^+e^-\to\phi\eta^\prime$. The Bellecollaboration has also determined$\mathcal{B}^{\phi(2170)}_{\phi\eta}\Gamma^{\phi(2170)}_{e^+e^-}$ morerecently, although the statistical significance related to the signal of$\phi(2170)$ in the data is low. We calculate the decay widths of $\phi(2170)$to $\phi\eta$ and $\phi\eta^\prime$, and compare their ratio$\Gamma^{\phi(2170)}_{\phi \eta}/\Gamma^{\phi(2170)}_{\phi \eta^\prime}$ withthe one determined by using the above mentioned experimental data. Consideringthe theoretical and experimental uncertainties, the lower limit of ourtheoretical result ($\simeq 2.6$) is close to the upper value obtained ($\simeq2$) by using the solution II of BESIII for$\mathcal{B}^{\phi(2170)}_{\phi\eta}\Gamma^{\phi(2170)}_{e^+e^-}$, as well asto the upper limit found ($\simeq 2.8$) when considering the solutions III andIV of the Belle collaboration for$\mathcal{B}^{\phi(2170)}_{\phi\eta}\Gamma^{\phi(2170)}_{e^+e^-}$.

$\phi(2170)$ decaying to $\phi\eta$ and $\phi\eta^\prime$