Data assimilation of flow measurements is an essential tool for extracting information in fluid dynamics problems. Recent works have shown that the physics-informed neural networks (PINNs) enable the reconstruction of unsteady fluid flows, governed by the Navier–Stokes equations, if the network is given enough flow measurements that are appropriately distributed in time and space. In many practical applications, however, experimental measurements involve only time-averaged quantities or their higher order statistics which are governed by the under-determined Reynolds-averaged Navier–Stokes (RANS) equations. In this study, we perform PINN-based reconstruction of time-averaged quantities of an unsteady flow from sparse velocity data. The applied technique leverages the time-averaged velocity data to infer unknown closure quantities (curl of unsteady RANS forcing), as well as to interpolate the fields from sparse measurements. Furthermore, the method’s capabilities are extended further to the assimilation of Reynolds stresses where PINNs successfully interpolate the data to complete the velocity as well as the stresses fields and gain insight into the pressure field of the investigated flow.