We investigate the nature of the near-threshold enhancement in the pp invariant mass spectrum of the reaction J/Ψ→γpp reported recently by the BES Collaboration. Using the Jülich NN model we show that the mass dependence of the pp spectrum close to the threshold can be reproduced by the S-wave pp final state interaction in the isospin I=1 state within the Watson-Migdal approach. However, because of our poor knowledge of the NN interaction near threshold and of the J/Ψ→γpp reaction mechanism and in view of the controversal situation in the decay J/Ψ→π 0 pp, where no obvious signs of a pp final state interaction are seen, explanations other than final state interactions cannot be ruled out at the present stage.