In the past decade, various quantitative phase microscopy (QPM) techniques have emerged, driven by the need to study biological samples non-invasively. However, the fundamental limit for phase noise is scarcely discussed in the literature. In a typically off-axis phase microscope system, the phase noise is limited to a few milliradians using a moderate camera. Common-path QPMs offer much reduced phase noise compared to typical Mach-Zehnder-based systems. However, further scaling down the phase noise becomes difficult. Here we propose a high-sensitivity common-path QPM that promises to reduce the phase noise by a factor of 10 (assuming the mechanical noise is negligible). This is achieved by a specifically designed signal filter, leaving only the subtle phase fluctuations coming from the dynamics sample scattering. By working at photon shot-noise limited detection, we can magnify the subtle phase contrast which is proportional to the camera well depth. We expect this system to have the height sensitivity similar to an atomic force microcopy, while measuring biological structures with a full field of view in a single-shot. We plan to use this system to study cell dynamics, particularly lamellipodial height fluctuations as well as stiffer cell membrane fluctuations.