You can find programs that can create an Android app that somewhat incorporates AVI movies. Can be some sort of live wallpaper, or similar app. It is not exactly conversion but more of an actual use of AVI in Android app.
Convert Audio Video Interleave movie to Google Android application package.
We have found one software suitable in our database for this conversion.
Microsoft Windows software - convert avi to apk on Windows
An Android wallpaper design app
Convert from avi file format
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.