Monodeuterated methanol is thought to form during the prestellar core stage of star formation. Observed variations in the CH2DOH/CH3OD ratio suggest that its formation is strongly dependent on the surrounding cloud conditions. Thus, it is a potential tracer of the physical conditions before the onset of star formation. A single-point physical model representative of a typical prestellar core is coupled to chemical models to investigate potential formation pathways toward deuterated methanol at the prestellar stage. Simple addition reactions of H and D are not able to reproduce observed abundances. The implementation of an experimentally verified abstraction scheme leads to the efficient formation of methyl-deuterated methanol, but lacks sufficient formation of hydroxy-deuterated methanol. CH3OD is most likely formed at a later evolutionary stage, potentially from H–D exchange reactions in warm ices between HDO (and D2O) and CH3OH. The CH2DOH/CH3OD ratio is not an appropriate tracer of the physical conditions during the prestellar stage, but might be better suited as a tracer of ice heating.