The translocator protein (TSPO) is a transmembrane protein present across the three domains of life. Its functional quaternary structure consists of one or more subunits. In mice, the dimer-to-monomer equilibrium is shifted in vitro towards the monomer by adding cholesterol, a natural component of mammalian membranes. Here, we present a coarse-grained molecular dynamics study on the mouse protein in the presence of a physiological content and of an excess of cholesterol. The latter turns out to weaken the interfaces of the dimer by clusterizing mostly at the inter-monomeric space and pushing the contact residues apart. It also increases the compactness and the rigidity of the monomer. These two factors might play a role for the experimentally observed incremented stability of the monomeric form with increased content of cholesterol. Comparison with simulations on bacterial proteins suggests that the effect of cholesterol is much less pronounced for the latter than for the mouse protein.