Unfortunately, I don’t think there is a possibility to supress the blue notification window at the moment. Would you like this feature to be added? (by means of an INI file switch)
All right mantra, I looked into the program and the option is already there!
Just add this line to the [AAVM] section of your avast! 4 file:
NeverShowInfo=1
This will suppress all blue info boxes that avast produces.
However, I’m not sure if this is what you want as now it won’t tell you e.g. even when a new program update is ready…