The nuclear multiple wobbling modes in A ≈60 mass region are explored by the adiabatic and configuration-fixed constrained covariant density functional theory for nickel isotopes for the first time. The potential-energy curves and deformation parameters β and γ of the ground and excited states of Ni-6257 are obtained to search for the possible wobbling candidates. It is shown that there are suitable triaxial deformations and high-j particle(s) or hole(s) configurations in Ni-6257, which are beneficial to the appearance of wobbling motion, including the simple, longitudinal and transverse modes. Moreover, possible multiple wobbling motions based on different high-j configurations might coexist in one single nucleus, which provides a promising basis for future experiments to find wobbling bands in the A ≈60 mass region. Finally, taking the nucleus 62Ni as an example, the experimental energy spectra, the angular momentum components, and the azimuthal plots are investigated by the combination of the covariant density functional theory and quantum particle rotor model. The transverse wobbling mode is suggested in this nucleus.