A sensitivity of the VEPP-2000 \(e^+e^-\) collider in a search for the rare decay \(\eta \rightarrow e^+ e^-\) has been studied. The inverse reaction \(e^+ e^- \rightarrow \eta\) is proposed for this search. We have analyzed a data sample with an integrated luminosity of 108 nb\(^{-1}\) collected with the SND detector in the center-of-mass energy range 520-580 MeV and found no background events for the reaction \(e^+ e^- \rightarrow \eta\) in the decay mode \(\eta\to\pi^0\pi^0\pi^0\). In the absence of background, a sensitivity to \({\cal B}(\eta \rightarrow e^+ e^-)\) of \(10^{-6}\) can be reached during two weeks of VEPP-2000 operation. Such a sensitivity is better than the current upper limit on \({\cal B}(\eta \rightarrow e^+ e^-)\) by a factor of 2.3.