cant see the list of databases in Feeds Database module UI tab
The documentation for this module is poor, but the solution is simple. 

The module picks up the $databases array defined in your settings.php file. In most installations, only one database 'default' is defined. Use the format for 'default' and define a second database say 'test', listing the correct connection credentials. The 'test' database will show up in the drop down. The module removes 'default' from the list because it makes no sense to map a database to itself.

I think better documentation for Feeds Database is in order :). However, the core Database API can be configured for multiple databases. See Database Configuration.