Time Machine destination

Welcome to Apple Support Communities.

Did you configure to use a volume on your internal drive as your Time Machine destination?

Time Machine should only be used to backup to external drives. If this is what you need to setup, I recommend purchasing a SanDisk Professional G-DRIVE - Western Digital or a G-Technology G-DRIVE mobile USB-C Portable Hard Drive - Apple.

Regardless of which drive you choose, it needs to be formatted. Follow these steps:

1. Go to Disk Utility (Finder > Go > Utilities)
2. In Disk Utility, select “View” > “Show All Devices”.
3. Select the top and non-indented drive in the external section of Disk Utility that matches the name of your external drive. 
4. Click Erase
5. Name: any name you want
6. Format: Use Mac OS Extended (Journaled) if you are using macOS Catalina or earlier, or APFS if you are using macOS Big Sur.
7. Scheme: GUID Partition Map
8. Click Erase

Finally, setup Time Machine: Back up your Mac with Time Machine - Apple Support.

Cheers,

Jack

You don't move it. Setup an external TM drive then send all the internal TM data to the trash. Once that's gone, start the TM backup to the external drive.