Surface plasmons supported by metallic nanostructures interact strongly with light and confine it into subwavelength volumes, thus forcing the corresponding electric field to vary within nanoscale distances. This results in exceedingly large field gradients that can be exploited to enhance the quadrupolar transitions of quantum emitters located in the vicinity of the nanostructure. Graphene nanostructures are ideally suited for this task, since their plasmons can confine light into substantially smaller volumes than equivalent excitations sustained by conventional plasmonic nanostructures. Furthermore, in addition to their geometric tunability, graphene plasmons can also be efficiently tuned by controlling the doping level of the nanostructure, which can be accomplished either chemically or electrostatically. Here, we provide a detailed investigation of the enhancement of the field gradient in the vicinity of different graphene nanostructures. Using rigorous solutions of Maxwell’s equations, as well as an analytic electrostatic approach, we analyze how this quantity is affected by the size, shape, doping level, and quality of the nanostructure. We investigate, as well, the performance of arrays of nanoribbons, which constitute a suitable platform for the experimental verification of our predictions. The results of this work bring new possibilities to enhance and control quadrupolar transitions of quantum emitters, which can find application in the detection of relevant chemical species, as well as in the design of novel light-emitting devices.