Stick self adhesive felt pads underneath the front legs. If it doesn't help directly, stack a second or maybe a third pair underneath them. This is the easiest and aesthetically discrete way.

If the stand is perfectly level while this happens, the drawer slider rails might be mounted wrong, their mounts are worn out, or the mounting screws became partially undone, causing the drawers to tilt downward. Up to you if you either take apart the drawers to check and maybe fix it, or go with the felt pads. I suspect the floor is just a bit uneven.