Medical image harmonization aims to transform the image 'style' among heterogeneous datasets while preserving the anatomical content. It enables data-sensitive learning-based approaches to fully leverage the data power of large multisite datasets with different image acquisitions. Recently, the attention mechanism has achieved excellent performance on the image-to-image (I2I) translation of natural images. In this work, we further explore the potential of leveraging the attention mechanism to improve the performance of medical image harmonization. Here, we introduce two attention-based frameworks with outstanding performance in the natural I2I scenario in the context of cross-scanner MRI harmonization for the first time. We compare them with the existing commonly used harmonization frameworks by evaluating their ability to enhance the performance of the downstream subcortical segmentation task on T1-weighted (T1w) MRI datasets from 1.5T vs. 3T scanners. Both qualitative and quantitative results prove that the attention mechanism contributes to a noticeable improvement in harmonization ability.