We investigate the role of the compact object in the production of jets from neutron star X-ray binaries. The goal is to quantify the effect of the neutron star spin, if any, in powering the jet. We compile all the available measures or estimates of the neutron star spin frequency in jet-detected neutron star X-ray binaries. We use as an estimate of the ranking jet power for each source the normalization of the power law which fits the X-ray/radio and X-ray/infrared luminosity correlations Lradio/IR∝LΓX (using infrared data for which there is evidence for jet emission). We find a possible relation between spin frequency and jet power (Spearman rank 97 per cent), when fitting the X-ray/radio luminosity correlation using a power law with slope 1.4; Γ= 1.4 is observed in 4U 1728-34 and is predicted for a radiatively efficient disc and a total jet power proportional to the mass accretion rate. If we use a slope of 0.6, as observed in Aql X-1, no significant relation is found. An indication for a similar positive correlation is also found for accreting millisecond X-ray pulsars (Spearman rank 92 per cent), if we fit the X-ray/infrared luminosity correlation using a power law with slope 1.4. While our use of the normalization of the luminosity correlations as a measure of the ranking jet power is subject to large uncertainties, no better proxy for the jet power is available. However, we urge caution in over-interpreting the spin-jet power correlations, particularly given the strong dependence of our result on the (highly uncertain) assumed power-law index of the luminosity correlations (which span less than 3 orders of magnitude in X-ray luminosity). We discuss the results in the framework of current models for jet formation in black holes and young stellar objects and speculate on possible different jet production mechanisms for neutron stars depending on the accretion mode.