Add internal page to admin menu

Yes, it’s possible.

First of all you need a way to identify the page. there are different way to do it: by page slug, by page template…

I suggest you to create a fucntion that retrieve that page.

Let’s assume the contact page has a page template called 'page-contacts.php'.

function get_contact_page() {
  $args = array(
    'number' => 1,
    'meta_key' => '_wp_page_template',
    'meta_value' => 'page-contacts.php'
  );
  $pages = get_pages($args);
  return ! empty( $pages ) ? array_pop($pages) : FALSE;
}

If you want to use a different way to identify your page, change this function accordingly.

After that, create a function to add the menu item hooking admin_menu:

function my_contact_page_menu() {
    $page = get_contact_page();
    if ( ! $page ) return;
    global $menu;
    $menu[] = array (
      'Contact Page', // menu label
      'manage_options', // capability
      get_edit_post_link( $page->ID, '' ),
      NULL,
      'menu-top menu-icon-post',
    );
}
add_action('admin_menu','my_contact_page_menu');