The femtoscopic $D_s^{+}{D}_s^{-}$ correlations are investigated to predict the signature of the not-yet-established $X(3960)$ state reported by the LHCb Collaboration in three scenarios: resonant, virtual, or bound. In the last two scenarios, it might also be identified as the state $X(3930)$. The formalism employed to generate this structure dynamically is based on the Bethe-Salpeter equation with a general $S$-wave potential. We investigate how the relevant properties and observables characterizing this state—such as the pole position, scattering length, and effective range—might be affected by variations in the model parameters. The amplitudes encoding the distinct interpretations of the $X(3960)$ state are then used as input to calculate the femtoscopic correlation function of the $D_s^{+}{D}_s^{-}$ pair, which is analyzed and discussed.