In recent years, deep neural networks have shown great potential in improving the speed and accuracy of medical image reconstruction. However, the practical application of these networks is often limited due to the need for large amounts of data and significant computational resources. Recently, untrained CNNs such as Deep Image Prior and ConvDecoder have produced impressive results in image reconstruction tasks without requiring any training data. In this study, we propose a new approach to improve the performance of an untrained neural network for magnetic resonance imaging (MRI) reconstruction. By incorporating an optimal transport function, we can efficiently transfer the statistical properties of a fully-sampled MRI image to a subsampled image without the need for additional training data. Our experimental results show that this approach outperforms existing state-of-the-art untrained techniques for accelerated MRI reconstruction. Additionally, using the optimal transport function significantly reduces the required computational resources, making it a promising avenue for accelerating MRI reconstruction in clinical settings.