The frequency of flooding in Venice has drastically increased over the last 50 years as a major consequence of natural and anthropogenic land subsidence, mean sea level rise, and a more active lagoon hydrodynamics induced partly by deepening of the largest navigation channels. Subsurface fluid injection is a well-established technology that is currently used either to enhance oil recovery from oil fields or to reduce land settlement due to hydrocarbon production. To help mitigate the inundation events in Venice, a numerical study of seawater injection into a 600--800 m deep geologic formation is performed with the aid of advanced numerical fluid dynamic and geomechanical models. A number of parametric scenarios are addressed, consistent with the basic geological configuration derived from the lithostratigraphy of nearby areas in the northern Adriatic basin. Preliminary quite encouraging results show that a set of 12 vertical injection wells, strategically located within the lagoon, may raise Venice from 11 to up to 40 cm over a 10 year period, thus offsetting or mitigating the vast majority of the high tides that occasionally plague the city. Further ad hoc geological and geophysical investigations of the lagoon subsurface are required before the present prefeasibility study can be turned into a design project of anthropogenic Venice uplift.