The characterization of the large amount of gas residing in the galaxy haloes, the so-called circumgalactic medium (CGM), is crucial to understand galaxy evolution across cosmic time. We focus here on the cool (T ∼ 104 K) phase of this medium around star-forming galaxies in the local Universe, whose properties and dynamics are poorly understood. We developed semi-analytical parametric models to describe the cool CGM as an outflow of gas clouds from the central galaxy, as a result of supernova explosions in the disc (galactic wind). The cloud motion is driven by the galaxy gravitational pull and by the interactions with the hot (T ∼ 106 K) coronal gas. Through a Bayesian analysis, we compare the predictions of our models with the data of the COS-Halos and COS-GASS surveys, which provide accurate kinematic information of the cool CGM around more than 40 low-redshift star-forming galaxies, probing distances up to the galaxy virial radii. Our findings clearly show that a supernova-driven outflow model is not suitable to describe the dynamics of the cool circumgalactic gas. Indeed, to reproduce the data, we need extreme scenarios, with initial outflow velocities and mass loading factors that would lead to unphysically high-energy coupling from the supernovae to the gas and with supernova efficiencies largely exceeding unity. This strongly suggests that, since the outflows cannot reproduce most of the cool gas absorbers, the latter are likely the result of cosmological inflow in the outer galaxy haloes, in analogy to what we have previously found for early-type galaxies.