We'll create fresh WordPress site with Featured Link Image installed. You have 20 minutes to test the plugin after that site we'll be deleted.
The plugin adds a meta box where you can upload or select an image from your media library.
After selection, the default Link Image field is populated with the image URL and a preview is available in the meta box.
The plugin also adds a Thumbnail column in the page /wp-admin/link-manager.php
Inspired by this question in WordPress Answers.
Português & Español