We studied the structural, electronic, and magnetic properties of a recently synthesized Ni(II)-quinonoid complex upon adsorption on a magnetic Co(001) substrate. Our density functional theory +U (DFT+U) calculations predict that the molecule undergoes a spin-state switching from low-spin S = 0 in the gas phase to high-spin S approximate to 1 when adsorbed on the Co(001) surface. A strong covalent interaction of the quinonoid rings and surface atoms leads to an increase of the Ni-O(N) bond lengths in the chemisorbed molecule that support the spin-state switching. Our DFT+U calculations show that the molecule is ferromagnetically coupled to the substrate. The Co surface-Ni center exchange mechanism was carefully investigated. We identified an indirect exchange interaction via the quinonoid ligands that stabilizes the molecule's spin moment in ferromagnetic alignment with the Co surface magnetization.