The theoretical and experimental description of fluid phase endocytosis (FPE) requires an asymmetry in phospholipid number between the two leaflets of the cell membrane, which provides the biomechanical torque needed to generate membrane budding. Although the motor force behind FPE is defined, its kinetic has yet to be determined. Based on a body of evidences suggesting that the mean surface tension is unlikely to be involved in endocytosis we decided to determine whether the cytosolic hydrostatic pressure could be involved, by considering a constant energy exchanged between the cytosol and the cell membrane. The theory is compared to existing experimental data obtained from FPE kinetic studies in living cells where altered phospholipid asymmetry or changes in the extracellular osmotic pressure have been investigated. The model demonstrates that FPE is dependent on the influx and efflux of vesicular volumes (i.e. vesicular volumes recycling) rather than the membrane tension of cells. We conclude that: (i) a relationship exists between membrane lipid number asymmetry and resting cytosolic pressure and (ii) the validity of Laplace's law is limited to cells incubated in a definite hypotonic regime. Finally, we discuss how the model could help clarifying elusive observations obtained from different fields and including: (a) the non-canonical shuttling of aquaporin in cells, (b) the relationship between high blood pressure and inflammation and (c) the mechanosensitivity of the sodium/proton exchanger.