Turbulent flow of purely viscoelastic fluids has gained attention in the drag-reduction and flow control communities since a tiny amount of polymer has proven efficient in reducing friction drag in pipe flows. Drag reduction by polymers (elasticity) is related to their ability to modify coherent structures in wall-bounded turbulence. When it comes to practical flows of interest, numerical simulations of such flows become challenging due to the associated computational cost of capturing the multiple physical mechanisms that drive the flow. On the other hand, experimental investigations of drag reduction in viscoelastic flows are limited by the near-wall measurements and the capability of the experimental techniques to accurately quantify the flow, without disturbing it. A complete description of viscoelastic turbulence would require the characterization of both velocity and polymeric stresses. However, the polymer deformation cannot be accessed directly from the experiments. Hence, in the objective of the present study, the idea of non-intrusive sensing has been applied to viscoelastic channel flow to predict the velocity fluctuations and polymeric stress components near the wall using the quantities measured at the wall. To this aim, the convolutional neural network (CNN) models are trained to predict the two-dimensional velocity fluctuation and polymeric shear stress fluctuation and elongation fields at different wall-normal distances in a viscoelastic channel flow. The present work would highlight the capability of a data-driven approach to model turbulence in complex fluid flows and in addition also finds useful applications in experimental settings.