We present an ultra-low temperature study (down to T=20 mK) of the nuclear spin-lattice relaxation (SLR) in the 55Mn nuclei of the molecular magnet Mn12-ac. The nuclear spins act as local probes for the electronic spin fluctuations, due to thermal excitations and to tunnelling events. In the quantum regime (below T≈0.75 K), the nuclear SLR becomes temperature independent and is driven by fluctuations of the cluster''s electronic spin due to the quantum tunnelling of magnetization in the ground doublet. The quantitative analysis of the nuclear SLR shows that the presence of fast-tunnelling molecules, combined with nuclear intercluster spin diffusion, plays an important role in the relaxation process. [Copyright &y& Elsevier]