A phone might prompt you for updates to applications or the phone’s software if newer software is available. However, it takes some room to download the update before the phone installs the update so some extra free space on the phone’s storage memory will be required.
Have you gone though and looked at what may be taking up some room on the phone? You can find a basic breakdown by going to Settings then Storage.
You can also take a look at this thread in the Tips and Tricks section about creating more room on the phone for yourself