While the preg_replace() works, it isn't the best method. The rel attribute should really only have the values alternate, author, bookmark, help, license, next, nofollow, noreferrer, prefetch, prev, or tag. (More info)
Instead, use the following class in your functions.php or plugin file to change the output so that the "Classes" field populates the <a> element instead of the <li> element.
class class_attr_nav extends Walker {
function start_el( &$output, $item, $depth = 0, $args = array(), $id = 0 ) {
$indent = ( $depth ) ? str_repeat( "\t", $depth ) : '';
$class_names = $value = '';
$classes = empty( $item->classes ) ? array() : (array) $item->classes;
$classes[] = 'menu-item-' . $item->ID;
$class_names = join( ' ', apply_filters( 'nav_menu_css_class', array_filter( $classes ), $item, $args ) );
$class_names = $class_names ? ' class="' . esc_attr( $class_names ) . '"' : '';
$id = apply_filters( 'nav_menu_item_id', 'menu-item-'. $item->ID, $item, $args );
$id = $id ? ' id="' . esc_attr( $id ) . '"' : '';
$attributes = ! empty( $item->attr_title ) ? ' title="' . esc_attr( $item->attr_title ) .'"' : '';
$attributes .= ! empty( $item->target ) ? ' target="' . esc_attr( $item->target ) .'"' : '';
$attributes .= ! empty( $item->xfn ) ? ' rel="' . esc_attr( $item->xfn ) .'"' : '';
$attributes .= ! empty( $item->url ) ? ' href="' . esc_attr( $item->url ) .'"' : '';
$attributes .= ! empty( $class_names ) ? ' class="' . esc_attr( $class_names ) .'"' : '';
$item_output = $args->before;
$item_output .= '<a'. $attributes .'>';
$item_output .= $args->link_before . apply_filters( 'the_title', $item->title, $item->ID ) . $args->link_after;
$item_output .= '</a>';
$item_output .= $args->after;
$output .= apply_filters( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args );
}
}
Then, when you want to display the menu, alter the wp_nav_menu() function to the following:
<?php wp_nav_menu( array( 'walker' => 'class_attr_nav' ) ); ?>