The synthesis of single-atom catalysts (SACs) is one of the main challenges in heterogeneous catalysis and electrocatalysis since it requires substrates with high thermal/chemical stability on which metal atoms can be stabilized without sintering. The present study introduces MXenes, a new class of two-dimensional materials involving transition-metal carbides, as feasible substrates for anchoring single-metal atoms. Using first-principles calculations based on the density functional theory, a systematic screening is performed including ten bare metal atoms of the 3d series and nine bare MXene surfaces with M2C stoichiometry (M = Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, and W). The results show that all 3d metal atoms interact exothermically with the MXene substrates and that the properties of the resulting M@MXene can be tuned by appropriately choosing the each of the two components. The analysis of the results indicates that it is possible not only to have atomically dispersed atoms at an MXene surface but also to control its charge (partially oxidized or partially reduced) state. In particular, Zn atoms anchored on MXenes appear as potential SAC candidates as clustering is not thermodynamically favored and surface diffusion is hindered by moderate energy barriers. Thus, the present results provide a rational guide to the design of new SAC catalysts based on MXenes.