We have performed ab initio calculations of a possible complex noncollinear magnetic structure in aluminium-rich Al-Mn liquids within the real-space tight-binding linear muffin-tin orbital method. In our previous work we predicted the existence of large magnetic moments in Al-Mn liquids [A. M. Bratkovsky, A. V. Smirnov, D. N. Manh, and A. Pasturel, Phys. Rev. B 52, 3056 (1995)], which has been very recently confirmed experimentally. Our present calculations show that there is a strong tendency for the moments on Mn to have a noncollinear (random) order retaining their large value of about 3 mu(B). The d electrons on Mn demonstrate a pronounced non-rigid-band behavior which cannot be reproduced within a simple Stoner picture. The origin of the magnetism in these systems is a topological disorder which drives the moments formation and frustrates their directions in the liquid phase.