The quasar remnant cores of nearby giant elliptical galaxies NGC 4486 (M87), 1399, 4649 and 4472 are the sites of supermassive (>109 M⊙) black holes. These objects are investigated as to the viability of the conjecture that they could harbour compact dynamos capable of generating the highest energy cosmic rays. For an accretion process involving an equipartition magnetic field near the event horizons of the underlying putative spun-up black holes, the energy achievable in accelerating protons could well be 1020 eV for all these galaxies when only considering the drag induced by curvature radiation. Estimates of the spectral energy distribution (SED) of ambient core photons lead to the conclusion that the energy losses arising from photo-pion production in proton collisions with these target photons are relatively small for all but M87. For M87, the ambient photon field is likely to be a limiting factor. Accretion rates of ∼1 M⊙ yr−1, comparable to the Bondi rates and to the stellar mass-loss rates, are associated with (>1020 eV) cosmic ray generation in the other (electromagnetically dark) galactic core sites. If these sites are found to be sources of such cosmic rays, it would suggest the presence of a global inflow of interstellar gas all the way into the centre of the host galaxy.