CCleaner, although part of Avast Software is a stand alone product.
Though I have no idea why CCleaner would give you this message (I haven't used CCleaner in many, many years), I don't know what settings you have in CCleaner that would monitor Running Programs to give this sort of message. So I would suggest checking the CCleaner settings. When I was using it, I did uncheck any monitoring/checking of the Avast Program.
The Avast Secure Browser (which I stopped using after testing) is also a stand alone product, though if you have Avast Antivirus installed there is some integration.
The Avast Secure Browser also has settings, 1) you can set it to be your default Browser and 2. to run on startup. So I don't know if either of those could possibly have this kind of effect/interaction with CCleaner.