The deposition of a prototypical spin-crossover [Fe(phen)2(NCS)2] complex on Au(111), Cu(111) and Ag(111) surfaces has been investigated by means of periodic DFT+U calculations, with the aim of understanding how different metallic surfaces affect the spin state switching. Our results show that adsorption is metal- and spin-dependent, with different preferred adsorption sites for the different surfaces and spin states. For the three considered surfaces adsorption energies are larger in the LS state than in the HS one, which increases the transition enthalpy by 58.7 kJ mol-1 for Cu(111), 14.6 kJ mol-1 for Au(111) and 9.6 kJ mol-1 for Ag(111) with respect to the free molecule. There is a clear correlation between this effect and the extent of the complex-surface interaction, which can be established from adsorption energies, surface-complex distances and charge density difference plots as: Cu(111) > Au(111) > Ag(111). Therefore, a stronger interaction with the surface produces a larger energy difference between two spin states, making the spin transition less probable to occur. Finally, our calculations show that it would be possible to probe the spin-state of the deposited molecules from the STM images, in line with the recent experimental results.