The Jetpack image widget allows you to add an image URL by copying it from an outside source or from your Media Library.
It would be nice to offer an option to search the Media Library for an image directly from the widget settings.
Original trac ticket:
In which case, swap the data store to stash the media ID rather than the URL.
It's probably best to focus our efforts on the Core widget now.
Agree on focusing on core widget for this. Closing.