Housing in Konstanz is in limited supply and high demand. This means you will need to actively search for it. If you have been looking for a while and not found anything suitable why not place an advertisement in a local newspaper? Continue to ask the people you know whether they know of anyone moving out of their current accommodation.
Use the university’s notice boards to let others know what kind of housing you are looking for.
You can even use social media to broaden your search even further.
Keep at it and remember that it may take a few months before you can find a suitable place to live.