My current total sent bytes almost doubles my total received bytes. If I don't reset my router, this will continue at an exponential rate. After a few hours my sent bytes will be almost 4 to 5 times more than my received and continue to climb.
I've tried to troubleshoot where all this sent information is coming from by running numerous virus/malware/rootkit scanners, of all different brands. AVG, Avast, SnD, Adaware, etc., netstat, all with zero unusual results.
I even unplugged all data cables from my router, reset the router, and then connected to it with my phone, which made things more confusing. After resetting and connecting with my phone, the router then began to use my phone to send a large amount of bytes.
What could be causing this? Could the router itself be piggybacking whatever is connected to it to send out information? If so, what could it possibly be sending in that manner?

Any help or insight is greatly appreciated.

Sadly, you told us absolutely nothing about the router. Make and model? Wired or wireless?

If it is the router, and no computer is connected to the router, then I don't see that any harmful (in terms of your identity being stolen) information could be sent out. But if your router is failing and just "chattering" away, your ISP may eventually get upset.

What if you bypass your router and connect your computer directly to your Internet gateway, typically the modem?