WordPress change author slug

I wonder if it is possible to change the author slug, not the author base slug.

I already changed the base slug with the following code:

add_action('init', 'cng_author_base');
function cng_author_base() {
    global $wp_rewrite;
    $author_slug = 'profile'; // change slug name
    $wp_rewrite->author_base = $author_slug;
}

It works perfectly, but now I’d like (if possible) change the author slug to ID

Eg. http://www.example.com/profile/{ID}

Any idea?
thank you