I've been reconnecting my equipment in my shack. I am currently running a Kenwood TS 2000. A few feet away I have a mini refrigerator. I'm still trying to troubleshoot the issue but it appears that when the refrigerator kicks on I hear a slight wine coming from the radio. The wine is present in receive mode as well as when you transmit. Obviously the solution is either Move either the Radio or get rid of the refrigerator. My goal is to keep both, however any ideas on how to eliminate the whining noise.

You're lucky - you have identified the source!
Half or more of the battle is won.

Are they plugged in to the same circuit? Can you change that and does it change the whine (even with an extension cord to see what happens).
Do you have snap on toroids to try? (These may or may not be good, but they are cheap and I snap them on all kinds of stuff.)
Do you have a toroid you can wind the power cord of either around? (Most likely the frig)

Easiest suggestions first!

Looks like the whine is still present even when the refrigerator does not kick on. I waited for the refrigerator to cycle down and the wine is still present during receive and transmit. I assume it's not normal for you to hear a slight whine when you transmit from the radio. It's very subtle but you can still hear it.

Is it present when the refrigerator is unplugged (trying to clarify).

Yes, and only on 70cm not on 2m.

Based on other thread, sounds like frig is not issue.

I suggest figuring out features of this rig you liked, consider upgrading to add a digital mode, buying used rig to replace.