The murmur produced by the speaker and captured by the Non-Audible Murmur (NAM)-one of the Silent Speech Interface (SSI) technique, suffers from the speech quality degradation. This is due to the lack of radiation effect at the lips and lowpass nature of the soft tissue, which attenuates the high frequencyrelated information. In this work, a novel method for NAM-to-Whisper (NAM2WHSP) speech conversion incorporating Generative Adversarial Network (GAN) is proposed. The GAN minimizes the distributional divergence between the whispered speech and the generated speech parameters (through adversarial optimization). The objective and subjective evaluation performed on the proposed system, justifies the ability of adversarial optimization over Maximum Likelihood (ML)-based optimization networks, such as a Deep Neural Network (DNN), in preserving and improving the speech quality and intelligibility. The adversarial optimization learns the mapping function with 54.2 % relative improvement in MOS and 29.83 % absolute reduction in % WER w.r.t. the state-of-the-art mapping techniques. Furthermore, we evaluated the proposed framework by analyzing the level of contextual information and the number of training utterances required for optimizing the network parameters, for the given task and database.