Why does Time Machine settings not see a network drive?

An external drive on a router is not a supported Time Machine back up disc.

Backup disks for Time Machine - Apple Support

A NAS that supports the “Time Machine over SMB” specification is a supported backup disk. If the router runs a file server that supports the “Time Machine over SMB” specification it might work, but it is still not supported by Apple.

The network drive format is irrelevant. A network backup is stored in a Sparse Bundle disk image which is formatted appropriately for a Time Machine backup.

All that being said, try mounting your Time Machine share in Finder, then try adding it as the Time Machine destination disk.

I had the same issue with a qnap NAS. I solved it by setting the SMB Protocol on the NAS to Version 3.

On qnap this could be done by the user interface:

[sorry Link remove, google for "QNAP SMB Time Machine"]

But the newest version of the firmware stopped showing this settings, after they fixed a security issue with SMB1. Luckily on can change this settings on the console by connecting to to the NAS using ssh:

ssh admin@mynas

That is what i did:

# setcfg -f /etc/config/smb.conf global "server min protocol" SMB2
# setcfg -f /etc/config/smb.conf global "min protocol" SMB2
# setcfg -f /etc/config/smb.conf global "server max protocol" SMB3
#  setcfg -f /etc/config/smb.conf global "max protocol" SMB3
# /etc/init.d/smb.sh restart

You have to be admin/root to do this.

You can see what is currently configured in this file:

/etc/config/smb.conf

For Qnap see here, just enable smb3 instead of SMB 1,as shown in the post:

[sorry Link remove: Google for "How to enable SMB v1 for QTS 4.2.6/4.3.3/4.3.4?"]

Doing this ended up showing my share in time machine settings:-)

There might be some other SMB requirements for the Time Machien to work, but i didn't find any in the apple documentation. So maybe i was just lucky to get the rest right.

I am seeing a similar problem though it might not be due to the same root cause.

I have been using a Synology NAS running the latest DSM (currently 7.2.xxx) with Time Machine configured to use a specific share name and user account dedicated for macOS Time Machine backups. The system is configured to use SMB 3.0 as the default.

I experienced a problem with the previous Time Machine store becoming corrupted and no longer usable. I therefore renamed that share marking it as hidden and created a new one of the same name as the original with access granted to the same user account.

Subsequently, both systems had been restarted. macOS (v14.5) Finder had no difficulty with seeing the new list of SMB network shares, but TimeMachine had cached the old share list. It was seeing the renamed share (which was now hidden), and was not listing the newly created Time Machine network share. The current list of network shares was also visible to "smbutil view". Neither Finder nor smbutil listed the former Time Machine share that had been renamed.

If I mounted the new Time Machine network share in Finder, the new share name would appear in the list displayed by Time Machine, but as soon as I unmounted the the new share in Finder, it would disappear from the list of network shares displayed by Time Machine.

I am currently waiting to see if the list will eventually refresh of its own accord, but there is clearly some problem with the caching of network share names in Time Machine. If the list in Time Machine is not refreshed after a few hours it looks like ANOTHER restart of macOS will be required to try and resolve problems with its caching of SMB network share names.

The router does have "Time Machine support over SMB" but for some reason, the Time Machine settings are not seeing it, hence my question: Why not?

I couldn't find that anywhere in their documentation, but it normally doesn't stop the drive from being used.

As I wrote in the post, the drive is accessible via "Connect to server" and browsing the network but Time Machine does not see the drive.

Yeah, I read that. Everything that normally works isn't working for you.