System Information
Operating system: Linux-5.4.0-54-generic-x86_64-with-debian-buster-sid 64 Bits
Graphics card: AMD Radeon VII

Blender Version
Broken: version: 2.91.0, branch: master, commit date: 2020-11-25 08:34, hash: rB0f45cab862b8

Exact steps for others to reproduce the error
Duplicate default cube, move it away somewhat.
Select either cube, go into object properties, right click and add driver to a transform channel.
Set the driver variable to "transform channel".
Attempt to use the eyedropper in the "Object" field of the variable to select the other cube.

It doesn't work, as moving the mouse out of the driver editor closes the driver editor.

In my opinion, the driver editor should have a close button that must be clicked. It should not close on "mouse-out", as you might be using the eyedroppers or moving through other parts of the UI (or even other applications) to get values to copy-paste into the fields. It should be (somewhat) more of a first-class window then it is.