One of the generic designs of the nuclear fusion DEMO reactor proposed by the EUROfusion consortium foresees the development of a tritium breeding blanket (BB) relying on the use of the liquid-metal PbLi eutectic alloy as both neutron multiplier and tritium breeder, namely the water-cooled lithium lead (WCLL) BB, whose strengths and weaknesses are well known. This paper focuses the attention on one of the possible disadvantages of such a technology: the production of the highly radiotoxic radionuclide 210Po, which could become a safety issue to be accounted for. The 210Po concentration within the PbLi circuit has been assessed by solving a modified version of Bateman's equations to consider the alloy circulation, so a one-dimensional convective fluid-dynamic model has been set up. Nuclear quantities have been evaluated by Monte Carlo neutron transport analyses using MCNP code and adopting a fully heterogeneous model of DEMO equipped with the WCLL BB. Moreover, rough sensitivity analyses have been performed to assess the influence on the results of the uncertainties related to the 209Bi radiative-capture cross section and the initial concentration of this nuclide which is present in the PbLi as an impurity. Results obtained have been critically discussed and some safety issues have been addressed to evaluate the possible hazard in case of a leak of PbLi accident.