Neural-network models have been employed to predict the instantaneous flow close to the wall in a viscoelastic turbulent channel flow. The numerical simulation data at the wall is utilized to predict the instantaneous velocity fluctuations and polymeric-stress fluctuations at three different wall-normal positions. Apart from predicting the velocity fluctuations well in a hibernating flow, the neural-network models are also shown to predict the polymeric shear stress and the trace of the polymeric stresses at a given wall-normal location with reasonably good accuracy. These non-intrusive sensing models can be integrated in an experimental setting to construct the polymeric-stress field in turbulent flows, which otherwise may not be directly quantifiable in experimental measurements.