The best way to store potato soup will depend on whether it's freshly made or leftovers. If you have freshly made soup that you want to store, it's best to let it cool to room temperature before transferring it to an airtight container and storing it in the refrigerator for up to three days. If you have leftovers, it's best to store them in an airtight container in the refrigerator and eat them within three days.