The possibility to graft nano-objects directly on its surface makes graphene particularly appealing for device and sensing applications. Here we report the design and the realization of a novel device made by a graphene nanoconstriction decorated with TbPc(2) magnetic molecules (Pc = phthalocyananine), to electrically detect the magnetization reversal of the molecules in proximity with graphene. A magnetoconductivity signal as high as 20% is found for the spin reversal, revealing the uniaxial magnetic anisotropy of the TbPc(2) quantum magnets. These results depict the behavior of multiple-field-effect nanotransistors with sensitivity at the single-molecule level.