Well, as mentioned above only the widget has the built-in ability to add a custom CSS class (called current) to a post if we’re viewing it at the moment. Nor the shortcode nor the wpp_get_mostpopular() template tag have this feature.
A way to achieve this would be by using WPP’s filter hooks in conjunction with WordPress’ get_queried_object_id() function.
Here’s a quick example using the wpp_post filter hook:
function my_custom_wpp_html_markup( $original_post_html, $post_object, $instance ){
// Get current post / page ID
$post_id = ( is_single() || is_page() ) ? get_queried_object_id() : null;
$output = '<li class="' . ( $post_id && $post_id == $post_object->id ? "active" : "" ) . '"><a href="' . get_permalink( $post_object->id ) . '">' . $post_object->title . '</a></li>';
return $output;
}