Audio inpainting and audio declipping are important problems in audio signal processing, which are encountered in various practical applications. A number of approaches has been proposed in the literature to address these problems, most successful of which are based on sparsity of the audio signals in certain dictionary representations. Non-negative matrix factorization (NMF) is another powerful tool that has been successfully used in applications such as audio source separation. In this paper we propose a new algorithm that makes use of a low rank NMF model to perform audio inpainting and declipping. In addition to utilizing for the first time the NMF model to perform audio inpainting in presence of arbitrary losses in time domain, the proposed approach also introduces a novel way to enforce additional constraints on the signal magnitude in order to improve the performance in declipping applications. The proposed approach is shown to have a comparable performance with the state of the art dictionary based methods while providing a number of advantages.