Computationally efficient optimal solutions for selecting a subset of antennas to maximize the mutual information of a MIMO channel have eluded the practitioners due to its combinatorial nature, and the performance gap is widened with massive MIMO. In this work, recent advances in deep learning are leveraged to develop a deep neural network (DNN) based receive antenna selection solution for a given problem dimension. We detail the neural network structure and evaluate several relevant figures of merit via numerical simulations. This data-driven solution is shown to achieve near optimal mutual information in simple settings, but does not scale naturally with the problem dimension. For the practical scenario where the number of selected antennas is unknown a priori, hybrid greedy solutions are proposed which build on the DNN-based solution for a given dimension and then greedily increase or decrease the number of antennas to approximate the optimal solution of the new problem dimension. Numerical simulations demonstrate the effectiveness of the hybrid solutions.