  The behavior of the $\phi$ meson at finite density is studied, making use of
a QCD sum rule approach in combination with the maximum entropy method. It is
demonstrated that a possible mass shift of the $\phi$ in nuclear matter is
strongly correlated to the strangeness content of the nucleon, which is
proportional to the strange sigma term, $\sigma_{sN} = m_s \langle N |
\overline{s}s | N \rangle$. Our results furthermore show that, depending on the
value of $\sigma_{sN}$, the $\phi$ meson could receive both a positive or
negative mass shift at nuclear matter density. We find that these results
depend only weakly on potential modifications of the width of the $\phi$ meson
peak and on assumptions made on the behavior of four-quark condensates at
finite density. To check the stability of our findings, we take into account
several higher order corrections to the operator product expansion, including
$\alpha_s$-corrections, terms of higher order in the strange quark mass and
terms of higher twist that have not been considered in earlier works.
