Graphite-moderated nuclear reactors have already produced more than 250000 tons of irradiated nuclear graphite, or i-graphite, world-wide. The sustainability of this technology relies on the end-of-life management of its moderator, which is activated into a long-lived nuclear waste, by neutron fluxes, during operating time. In particular, C14 is created. Nuclear transmutation, enabled by laser-driven particle acceleration, has been envisioned as a potential novel treatment scheme for long-lived nuclear waste. By triggering controlled nuclear reactions with energetic particles, long-lived radionuclides could be transformed into stable isotopes. Such a system could treat the C14 nuclei trapped within the i-graphite matrix, which is difficult to isolate by other means. This work performs a quantitative preliminary study of this transmutation scheme, in order to assess its feasibility at an industrial scale. The method used can be transposed to assess any transmutation scheme using a beam of particles directly sent on the material to be treated. First, a nuclear interaction channel which transmutes C14 nuclei without creating new long-lived radionuclides is identified. It consists in the choice of a type of particle, among which protons, gamma photons and neutrons can all be accelerated by laser-matter interaction; and it is completed by the adequate energy at which this particle must be sent on i-graphite. To that end, the nuclear cross-sections of C12, C13 and C14 are reviewed, neglecting other impurities in i-graphite. Then, based on the interaction channel identification, the energy cost of this scheme is estimated. Protons between 1 and 5 MeV make it possible to transmute C14 without creating any new long-lived activity. However, our result show that, even in this favorable reaction channel, the transmutation energy cost is too high for an i-graphite transmutation scheme to be feasible.