Hi!
Well, this is only possible by results templating. If you read up on that knowledge base, it will explain some basic details.
Basically, you need to make a directory in your theme/child theme directory called asp. Then copy over the no-results.php file from the wp-content/plugins/ajax-search-pro/includes/views/results/ directory. Then making changes directly to this file is the key, as this is included when printing the ‘no results’ text. You can add the link or any custom HTML code in there.
I am not sure how experienced you are in coding, so I constructed a no-results.php file, which includes a link to that destination. You can change that on lines 31-33. Let me know if you need help with this.