Based on 87Sr/86Sr data of the Primary Lower Gypsum (PLG) deposits in the Vena del Gesso basin—a marginal basin of the Mediterranean during the Messinian Salinity Crisis—a correlation between 87Sr/86Sr values and precessional forcing has recently been proposed but not yet confirmed. In this study, a box model is set up to represent the Miocene Mediterranean deep basin and a connected marginal basin. Measurements of 87Sr/86Sr in the Vena del Gesso and estimated salinity extrema are used to constrain model results. In an extensive analysis with this model, we assess whether coeval 87Sr/86Sr and salinity fluctuations could have been forced by precession-driven changes in the fresh water budget. A comprehensive set of the controlling parameters is examined to assess the conditions under which precession-driven 87Sr/86Sr variations occur and to determine the most likely setting for PLG formation. Model results show that precession-driven 87Sr/86Sr and salinity fluctuations in marginal basins are produced in settings within a large range of marginal basin sizes, riverine strontium characteristics, amplitudes of precessional fresh water budget variation, and average fresh water budgets of both the marginal and deep basin. PLG deposition most likely occurred when the Atlantic-Mediterranean connection was restricted, and the average fresh water budget in the Mediterranean was significantly less negative than at present day. Considering the large range of settings in which salinities and 87Sr/86Sr fluctuate on a precessional timescale, 87Sr/86Sr variations are expected to be a common feature in PLG deposits in marginal basins of the Mediterranean.