Apple - Why can't Time Machine see shared drive?
When you click the "Options..." button in the File Sharing preferences, is "Share files and folders using AFP" enabled? Time Machine over the network requires AFP, so it won't work if only SMB is enabled.
You may also need to disable SMB. I am not exactly sure why this is the case, but sometimes the SMB share takes priority and Time Machine can't seem to see the AFP share. Note that this will prevent Windows clients from connecting to file shares.
Because your Shared drive is not a TimeMachine enabled shared volume.
TimeMachine have special requirements using AFP as pointed out by gabedwrds thus thoses (eg. AFP Replay Cache) are not necessarily included with "OSX Client".
You should enable a "TimeMachine Server" in order to share an external disk accross the network.
You may try using the Terminal if you are not prepared to buy "Server.app". But you're talking about data backup therefore you want to be sure about consistency and recoverability ! Other backup solutions such as the excellent "Carbon Copy Cloner can achieve this without the "Server.app" and you may get free of charges similar results by using the rsync command from the terminal or using Automator.app…
If you don't care about using an unsupported solution and you are willing to take the risk of being in the so called "poo" :
• Either show unsupported network volumes :
defaults write com.apple.systempreferences TMShowUnsupportedNetworkVolumes 1
And then have a look in your TimeMachine system preferences…
• Or inputing the shared volume name manually therefore in your case type in the terminal :
sudo tmutil setdestination /Volumes/MBA\ TM
Then start your first backup :
tmutil startbackup
How to make Time Machine backups over network without OS X server?
I know its an old post, but hopefully this will help anyone looking into the issue. Disabling SMB will work, but isn't necessary. OS X now uses SMB as the default connection (see here: http://www.cnet.com/news/os-x-mavericks-switches-to-smb2-networking/), and SMB doesn't work with Time Machine. You can either disable SMB, thus forcing the mac to connect with AFP, or you can use the Finder 'Connect to Server' button under the Go menu, and force AFP as the protocol. I.e. afp://myserver.domain Tested under Yosemite 10.10.3