My Book for Mac unable to use Time Machine when connected to a router

Using the provided USB cable, I plugged my new WD hard drive into my computer and followed the steps for installation. I then opened Disk Utility and verified the hard drive was mounted. I would now like to connect the WD hard drive, using the USB cable, to my router so I can wirelessly backup my data (preferably using Time Machine as the new hard drive says it is able to). I plugged the hard drive into the router’s USB and opened a browser to access the router using its IP address. The router recognizes the hard drive but says its “unmounted.” I then tried to use Time Machine to backup my data but with no success. I contacted my router manufacturer and after 30 minutes on hold and 60 minutes of what they called troubleshooting, I was instructed to call/contact WD to resolve the problem. They mentioned I might need to reformat the hard drive to NTFS rather than the HFS+ (Mac OS Extended (Journaled) it came with?
My Mac specs- El Capitan v10.11.2, 2.6 GHz Intel Core i7, 16 GB 1600 MHz DDR3 RAM
My Router Specs- ASUS RT-AC68U
My questions:
1- Is this HD compatible with my router (or vice versa)? 2- Does my HD actually need to be reformatted? 3- Is it even possible to connect this HD to my/a router for wireless backups?

Hi there,

I have not tried this, however you can check on yout router settings to see if there is any option to use on a mac so this way it can backup with time machine, lets see if another user can share some information or tips on this matter