If you do not have enough free space on the phone this could be the issue, have you tried using the computer to upgrade you iPhone?
What error are you getting if any? where does the phone indicate it cannot proceed with the update?
You can try purging your update file and re downloading by doing the following:
1. Go to Settings > General > [Device name] Storage.
3. Find the update in the list of apps.
4. Tap the update, then tap Delete Update.
5. Go to Settings > General > Software Update and download the latest update.