Upgrade WordPress without FTP

Open /wp-config.php

Now the first thing you need to do is to open the wp-config.php file from your WordPress root folder (you may access this file from your WordPress installer folder). From the installation folder, the file is located at wordpress/wp-config.php

Insert FS_METHOD

Paste the following code to your wp-config.php file, preferably just below every other line of code.

define('FS_METHOD','direct');

Save and Try updating now. If you have inappropriate directory and file permission, might  encounter upgrade error. Try to do the following-

Web Server Ownership

The first level is actually to make sure that your web server has ownership over the directories:

chown -R www-data:www-data your-wordpress-directory

Directory Permissions

The second level is also required – you must make sure that the directory permissions are properly set:

sudo find /var/www/wordpress/ -type d -exec chmod 755 {} \; 
sudo find /var/www/wordpress/ -type f -exec chmod 644 {} \;
sudo chown -R www-data:www-data wp-content/plugins/
sudo chmod 775 wp-content
sudo chown -R www-data:www-data wp-content/