Walker! Throw in functions.php

walker.php

class Walker_Nav_Menu_Dropdown extends Walker_Nav_Menu{
    function start_lvl(&$output, $depth){
      $indent = str_repeat("\t", $depth); // don't output children opening tag (`<ul>`)
    }

    function end_lvl(&$output, $depth){
      $indent = str_repeat("\t", $depth); // don't output children closing tag
    }

    function start_el(&$output, $item, $depth, $args){
      // add spacing to the title based on the depth
      $item->title = str_repeat("&nbsp;", $depth * 4).$item->title;

        $output .= $indent . ' <select id="menu-item-'. $item->ID . '"' . $value . $class_names .'>';  
        // $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 )        ? ' value="'   . esc_attr( $item->url        ) .'"' : '';  
        
        $item_output .= '<option'. $attributes .'>';  
        $item_output .= $args->link_before .apply_filters( 'the_title', $item->title, $item->ID );  
        $item_output .= '</option>';  
        
        $output .= apply_filters( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args );  

      // no point redefining this method too, we just replace the li tag...
      // $output = str_replace('<li', '<option', $output);
    }

    function end_el(&$output, $item, $depth){
      $output .= "</option>\n"; // replace closing </li> with the option tag
    }
}