When backing up for the first time with OS Sierra, The Time Machine (TM) will require enormous storage on the backup drive. The whole content of the computer will need to be backed up afresh (it won't do a piggy back 'top-up' on the old backup by the previous OS).
This is how I solved the problem (I am now on Sierra 10.12.1):
1) Stop back-up that is stuck on “Preparing to back-up”. If the preparation and the backup don't start in under a minute, TM is asking for more storage.
2) Check storage available:
2a) On top right of the screen:
Time machine preferences > On bottom right, Preferences > Check “Estimated size of full backup: - -” You will need that much space on the hard-drive to do the first back up with the new OS Sierra.
2b) Alternatively, you may find out how much data has been stored on the Mac (the whole of it will need to be backed up!).
Top left of the screen:
Click on the Apple icon on > About this Mac > On top of the new window choose Storage. You will need that much storage (perhaps much more for future top-ups) on the Time Machine hard-drive for the first backup.
2c) Right click on the TM hard-drive on the screen, choose “Get Info” and check whether there is enough storage avaiable for the backup.
You will find that there isn't.
3) If you now need to backup:
This is now possible only if you have a choice of another place to store (backup), like a larger partition of the same hard-drive or another hard drive.
You will need to choose one of the above:
3a) On top of the screen click on the TM icon > Open Time Machine Preferences. > Select Disk: one of the above two choices (larger partition of the same hard-drive or another hard-drive connected to the Mac) that has enough storage (and more) for the entire data on the computer.
I chose the other partition on the hard-drive. (I didn't need to re-format.) One partition I was using for TM and the other for “drag-and-drop” manual backup of certain files; I chose the latter, which had plenty of space.
3b) Choose the back-up to be done on the new drive replacing the old one.
4) Now back up as usual. It could take several hours to finish backing up.
Best of luck.