The origin of the magnetic field in massive O-type stars is still under debate. To model the physical processes responsible for the generation of O star magnetic fields, it is important to understand whether correlations between the presence of a magnetic field and stellar evolutionary state, rotation velocity, kinematical status, and surface composition can be identified. The O4 Ief supergiant zeta Pup is a fast rotator and a runaway star, which may be a product of a past binary interaction, possibly having had an encounter with the cluster Trumper 10 some 2 Myr ago. The currently available observational material suggests that certain observed phenomena in this star may be related to the presence of a magnetic field. We acquired spectropolarimetric observations of zeta Pup with FORS 2 mounted on the 8 m Antu telescope of the Very Large Telescope to investigate if a magnetic field is indeed present in this star. We show that many spectral lines are highly variable and probably vary with the recently detected period of 1.78 day. No magnetic field is detected in zeta Pup, as no magnetic field measurement has a significance level higher than 2.4 sigma. Still, we studied the probability of a single sinusoidal explaining the variation of the longitudinal magnetic field measurements.