  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 recently
determined by the BESIII, BaBar and Belle collaborations with the aim of
unraveling the nature of $\phi(2170)$. By analyzing the data on the cross
sections of the process $e^+e^-\to\phi\eta$, two solutions were found by the
BESIII collaboration with the same $\chi^2/n.d.f$, mass and width for
$\phi(2170)$. However, different values for
$\mathcal{B}^{\phi(2170)}_{\phi\eta}\Gamma^{\phi(2170)}_{e^+e^-}$ were
obtained: $0.24^{+0.12}_{-0.07}$ eV (solution I) and $10.11^{+3.87}_{-3.13}$ eV
(solution II). In case of
$\mathcal{B}^{\phi(2170)}_{\phi\eta^\prime}\Gamma^{\phi(2170)}_{e^+e^-}$, a
value of $7.1\pm 0.7\pm 0.7$ was determined by the BESIII collaboration from
fits to the data on the cross section of $e^+e^-\to\phi\eta^\prime$. The Belle
collaboration has also determined
$\mathcal{B}^{\phi(2170)}_{\phi\eta}\Gamma^{\phi(2170)}_{e^+e^-}$ more
recently, 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
$\Gamma^{\phi(2170)}_{\phi \eta}/\Gamma^{\phi(2170)}_{\phi \eta^\prime}$ with
the one determined by using the above mentioned experimental data. Considering
the theoretical and experimental uncertainties, the lower limit of our
theoretical result ($\simeq 2.6$) is close to the upper value obtained ($\simeq
2$) by using the solution II of BESIII for
$\mathcal{B}^{\phi(2170)}_{\phi\eta}\Gamma^{\phi(2170)}_{e^+e^-}$, as well as
to the upper limit found ($\simeq 2.8$) when considering the solutions III and
IV of the Belle collaboration for
$\mathcal{B}^{\phi(2170)}_{\phi\eta}\Gamma^{\phi(2170)}_{e^+e^-}$.
