A low intensity light beam emerges from a graded-index, highly multimode optical fibre with a speckled shape, while at higher intensity the Kerr nonlinearity may induce a spontaneous spatial self-cleaning of the beam. Here, we reveal that we can generate two self-cleaned beams with a mutual coherence large enough to produce a clear stable fringe pattern at the output of a nonlinear interferometer. The two beams are pumped by the same input laser, yet are self-cleaned into independent multimode fibres. We thus prove that the self-cleaning mechanism preserves the beams' mutual coherence via a noise-free parametric process. While directly related to the initial pump coherence, the emergence of nonlinear spatial coherence is achieved without additional noise, even for self-cleaning obtained on different modes, and in spite of the fibre structural disorder originating from intrinsic imperfections or external perturbations. Our discovery may impact theoretical approaches on wave condensation, and open new opportunities for coherent beam combining.