Place below code in functions.php

<?php

add_filter(‘wp_nav_menu_items’, ‘add_login_logout_link’, 10, 2);
function add_login_logout_link($items, $args) {
ob_start();
wp_loginout(‘index.php’);
$loginoutlink = ob_get_contents();
ob_end_clean();
$items .= ‘<li>’. $loginoutlink .'</li>’;
return $items;
}

?>