The possibility of diquark condensation at sufficiently large baryon chemical potential and zero temperature is analyzed in QCD at strong coupling. In agreement with other strong coupling analysis, it is found that a first order phase transition separates a low density phase with chiral symmetry spontaneously broken from a high density phase where chiral symmetry is restored. In none of the phases diquark condensation takes place as an equilibrium state, but, for any value of the chemical potential, there is a metastable state characterized by a non-vanishing diquark condensate. The energy difference between this metastable state and the equilibrium state decreases with the chemical potential and is minimum in the high density phase. The results indicate that there is attraction in the quark-quark sector also at strong coupling, and that the attraction is more effective at high baryon density, but for infinite coupling it is not enough to produce diquark condensation. It is argued that the absence of diquark condensation is not a peculiarity of the strong coupling limit, but persists at sufficiently large finite couplings.