In this paper, the kinetics of ordering of an assembly of non-interacting nanorods suspended in a solidifying liquid film is studied theoretically. Assuming random orientation of nanorods at the initial moment of time, the time needed for nanorods to align along the direction of an external magnetic field is estimated. In the solidifying films with exponentially increasing viscosity, the viscous drag significantly resists the nanorod alignment. Therefore, some nanorods might be quenched halfway to the equilibrium orientation even before complete solidification of the film. Different regimes of ordering have been revealed and classified and the criterion for the alignment of nanorods prior to the film solidification has been introduced.