$wpdb prepare issue with mysql DATE_FORMAT

From the Codex page for the WPDB class:

[…] the prepare method […] supports both a sprintf()-like and vsprintf()-like syntax.

Having a look at PHP’s documentation for sprintf():

##Example 6

   // notice the double %%, this prints a literal '%' character

So you can use

$result = $wpdb->get_var( 
  $wpdb->prepare(
    "SELECT DATE_FORMAT(report_date, '%%d-%%m-%%Y') FROM table WHERE report_id = %d",
     $report_id 
   )
);

for your purposes.