In this paper we have tried to understand the nature of magnetism in ZnO nanoparticle samples with an intrinsic 50 ppm trace of Fe impurity. When the samples are annealed we observe formation of nanoparticle agglomerates and the size increases with annealing temperature. When the sample is annealed at 600 °C we observe superparamagnetic behaviour, and the magnetic hysteresis along with the coercive field below the blocking temperature is almost independent of the cooling field. When the sample is annealed at 900 °C we observe reduction of saturation magnetization but the magnetic hysteresis and the coercive field are now dependent on the cooling field, indicating magnetic correlation and ordering within the agglomerated nanograins. We propose a simple model that explains the reduction of magnetization as being due to a vortex-state-like flux closure formation.