You can try the edit_form_after_title action:
add_action( 'edit_form_after_title', function(){
echo '<hr/><div>My custom HTML</div><hr/>';
});
to add your custom HTML after the permalink:
It will inject the HTML between div#titlediv and div#postdivrich:
<div id="post-body-content">
<div id="titlediv">...<!-- /titlediv -->
<hr><div>My custom HTML</div><hr>
<div id="postdivrich" class="postarea edit-form-section">...</div>
...
</div>
Tip: when you have question like this, best thing to do is look at source code.
The file responsible to output post edit page in admin is /wp-admin/edit-form-advanced.php
The hook you are looking for is 'edit_form_after_title' as you can see at line #476 of that file.