Machine unlearning (MU) has gradually become an independent and innovative approach in artificial intelligence (AI) that removes any undesirable training set from a pre-trained model. The researchers first applied machine unlearning to classification and recommendation use cases. However, new findings have shown that machine unlearning is viable in medical imaging, particularly in MRI reconstruction. This work aims to determine when and how it is feasible to unlearn MRI medical data, a task that is faced with issues of privacy, computational cost, and accuracy. We discuss and compare major algorithms, their advantages and disadvantages, the specific limitations of MR imaging, and ways to address them. The study also recounts other publicly accessible MRI datasets, such as the UK Biobank and OASIS databases, and their properties for machine unlearning research. In addition, the effectiveness of the presented machine unlearning methods is assessed in the context of the degradation of model performance trained on these datasets with a focus on privacy and utility trade-offs. The insights obtained from our work can help in improving the machine unlearning process for medical imaging to satisfy the most data privacy protection laws while incurring minimal loss in the accuracy of the model.