I know this is an old thread, but this nag has finally worn me down to the point where I needed to look for a fix... which brought me here. So, I tried some of things listed here, but also tried one of my own that was NOT listed. Whatever I did, it appears to be working for now, but time will tell.
- Fixes from here: Options | Save | uncheck the box for autosave to the cloud. Since I don't use SharePoint and only occasionally need OD, I unchecked it. May not be the answer.
-- while in here, I also made sure "Save to Computer by default" was checked. Maybe it will stop trying to look for the cloud as the first choice which annoyed me. I can't figure out why I hadn't changed that before now.
-- there was another fix suggested in reference to "Microsoft Experience" found in the About | Account Settings. Unchecked all of those. Don't need any suggestions from MS.
My fix: stop OneDrive from automatically starting up in the first place. You can't right-click it in the task area and Exit. You have to stop the auto-start. Task Manager | Startup tab | find OneDrive, right-click, disable. After all the fixes, I restarted the computer. Maybe if it's not running in the background, MS products will stop trying to use it. Maybe.
I use OD occasionally so I didn't want to completely uninstall. But I don't need it running full time. If I need it, I'll run OD, do what I need to do, then restart the computer to kill it off again.
Something in all of the "fixes" I did seem to be having an effect. I've opened multiple Excel and Word files and haven't been prompted yet. Normally, it prompts right away. But like I said, time will tell.