In the advent of a digital health revolution, vast amounts of clinical data are being generated, stored and processed on a daily basis. This has made the storage and retrieval of large volumes of health-care data, especially, high-resolution medical images, particularly challenging. Effective image compression for medical images thus plays a vital role in today's healthcare information system, particularly in teleradiology. In this work, an X-ray image compression method based on a Convolutional Recurrent Neural Networks RNN-Conv is presented. The proposed architecture can provide variable compression rates during deployment while it requires each network to be trained only once for a specific dimension of X-ray images. The model uses a multi-level pooling scheme that learns contextualized features for effective compression. We perform our image compression experiments on the National Institute of Health (NIH) ChestX-ray8 dataset and compare the performance of the proposed architecture with a state-of-the-art RNN based technique and JPEG 2000. The experimental results depict improved compression performance achieved by the proposed method in terms of Structural Similarity Index (SSIM) and Peak Signal-to-Noise Ratio (PSNR) metrics. To the best of our knowledge, this is the first reported evaluation on using a deep convolutional RNN for medical image compression.