We obtained multi-epoch Very Large Telescope optical spectroscopic data in 2011 and 2012 on the ultraluminous X-ray source NGC 5408 X-1. We confirm that the He II λ4686 line has a broad component with an average full width at half-maximum of v = 780 ± 64 km s-1 with a variation of ˜13 per cent during observations spanning over four years, and is consistent with the origin in the accretion disc. The deepest optical spectrum does not reveal any absorption line from a donor star. Our aim was to measure the radial velocity curve and estimate the parameters of the binary system. We find an upper limit on the semi-amplitude of the radial velocity of K = 132 ± 42 km s-1. A search for a periodic signal in the data resulted in no statistically significant period. The mass function and constraints on the binary system imply a black hole mass of less than ˜510 M⊙. Whilst, a disc irradiation model may imply a black hole mass smaller than ˜431-1985 M⊙, depending on inclination. Our data can also be consistent with an unexplored orbital period range from a couple of hours to a few days, thus with a stellar-mass black hole and a subgiant companion.