Among all transition metals, palladium (Pd) has the highest density of states at the Fermi energy at low temperatures yet does not fulfill the Stoner criterion for ferromagnetism. However, close proximity to magnetism renders it a nearly ferromagnetic metal, which hosts paramagnons, strongly damped spin fluctuations. Here we compare the total and the differential conductance of monoatomic contacts consisting of single Pd and cobalt (Co) atoms between Pd electrodes. Transport measurements reveal a conductance for Co of 1G(0), while for Pd we obtain 2G(0). The differential conductance of monoatomic Pd contacts shows a reduction with increasing bias, which gives rise to a peculiar Lambda-shaped spectrum. Supported by theoretical calculations, we correlate this finding with the lifetime of hot quasiparticles in Pd, which is strongly influenced by paramagnon scattering. In contrast to this, Co adatoms locally induce magnetic order, and transport through single cobalt atoms remains unaffected by paramagnon scattering, consistent with theory.