We discuss a model of spontaneous collapse of the quantum state that does not require adding any stochastic processes to the standard dynamics. The additional ingredient with respect to the wave function is a position in the configuration space, which drives the collapse in a completely deterministic way. This new variable is equivalent to a set of positions of all the particles, i.e. a set of Bohmian positions, which obey the usual guiding equation of Bohmian theory. Any superposition of quantum states of a macroscopic object occupying different regions of space is projected by a localization process onto the region occupied by the positions. Since the Bohmian positions are well defined in a single realization of the experiment, a space localization into one region is produced. The mechanism is based on the correlations between these positions arising from the cohesive forces inside macroscopic objects. With appropriate values of the two parameters of the model, we check that the corresponding dynamics rapidly projects superpositions of macroscopic states localized in different regions of space into a single region, while is keeps a negligible effect in all situations where the predictions of standard quantum dynamics are known to be correct. The possible relations with gravity are briefly speculated. We then study the evolution of the density operator and a mean-field approximation of the dynamical equations of this model, as well as the change of the evolution of the momentum introduced by the localization process. Possible theoretical interpretations are finally discussed. Generally speaking, this model introduces a sharper border between the quantum and classical world than the GRW and CSL theories, and leaves a broader range of acceptable values for the parameters.