Deep learning (DL)-based models are the most widely used machine learning models which have been applied to solve numerous problems in high-energy particle physics. The ability of the DL models to learn unique patterns and correlations from data to map highly complex nonlinear functions is a matter of interest. Such features of the DL model could be used to explore the hidden physics laws that govern particle production, anisotropic flow, and spectra in heavy-ion collisions. This work sheds light on the possible use of the DL techniques, such as the feed-forward deep neural network (DNN) based estimator, to predict the elliptic flow ($v_2$) in heavy-ion collisions at RHIC and LHC energies. A novel method is used to process the track-level information as input to the DNN model. The model is trained with Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV minimum bias simulated events with AMPT event generator. The trained model is successfully applied to estimate the centrality dependence of $v_2$ for both LHC and RHIC energies. The proposed model is quite successful in predicting the transverse momentum ($p_{\rm T}$) dependence of $v_2$ as well. A noise sensitivity test is performed to estimate the systematic uncertainty of this method. The results of the DNN estimator are compared to both simulation and experiment, which concludes the robustness and prediction accuracy of the model.