Fluorographene quantum dots prepared from fluorinated graphene oxide (FGO) show a linear dependence of the magnetization on the applied field. This is further supported by DFT calculations taking into account a few possible systems of functionalized graphene quantum dots. The inherent magnetism, high concentration of fluorine and cyto-compatibility of these quantum dots promise potential application as a dual modal agent for proton and 19F based Magnetic Resonance Imaging which is investigated here. A metal free dual modal contrast agent would bring about a great change in the efficiency and resolution of this widely used imaging tool.