A unique property of metal nanoclusters is the superatom shell structure of their delocalized electrons. The electronic shell levels are highly degenerate and therefore represent sharp peaks in the density of states. This can enable exceptionally strong electron pairing in certain clusters composed of tens to hundreds of atoms. In a finite system, such as a free nanocluster or a nucleus, pairing is observed most clearly via its effect on the energy spectrum of the constituent fermions. Accordingly, we performed a photoionization spectroscopy study of size-resolved aluminum nanoclusters and observed a rapid rise of the near-threshold density of states of several clusters ($Al_{37,44,66,68}$) with decreasing temperature. The characteristics of this behavior are consistent with compression of the density of states by a pairing transition into a high-temperature superconducting state with $T_c$>~100 K. This value exceeds that of bulk aluminum by two orders of magnitude. These results highlight the potential of novel pairing effects in size-quantized systems and the possibility to attain even higher critical temperatures by optimizing the particles size and composition. As a new class of high-temperature superconductors, such metal nanocluster particles are promising building blocks for high-$T_c$ materials, devices, and networks.