Retrieving Author ID in wp-admin area

It can be done like this without having to rely on the $post global.

if ( is_admin() ) {
    if( isset( $_GET['post'] ) && isset( $_GET['action'] ) && $_GET['action'] === 'edit' ) {
        $post_id = $_GET['post'];
        $current_post = get_post($post_id);
        $author_id = $current_post->post_author;
    } 
}

The query string variable post is always the post_id you are editing and additionally you need to check if the action query variable is set and it equals to edit.

Additionally you can explore the get_current_screen() function to setup more advanced conditionals for better security.