I have a noisy drive train on my Trek road bike with Shimano 105. It's very noticeable on the big cog, and is not as bad on the small cog, but still irritating. It's just a constant whiring noise. I am going to give it a clean all around, but it is really not too dirty at all at the moment, and i don't think that will be the solution. Any ideas where else to look?
I would recommend, as you stated you were already doing, that you give your driving mech a full cleaning. Run some hot water and a degreaser through all of your gears and your chain, (thoroughly). After that, (it helps if you have a repair stand for this), take some nice chain oil and run it on your chain real good, then shift through all of your gears and run that lube thoroughly through your gears. Personally, I do this two or three times to make sure everything is well lubed. Don't use too much, but dont be stingy with it either. Also, be sure you lube both sides of the chain.
I'm sure the mech itself is ok, but maybe it would be good to check and make sure your front and rear dérailleur are clean so that your shifting is smooth. Also check to make sure your gears are indexed correctly.
Hopefully something here helps you out. Good luck!