Just a quick change to wp-config.php
define('FS_METHOD','direct');
That’s it, enjoy your wordpress updates without ftp!
Alternate Method:
There are hosts out there that will prevent this method from working to ease your WordPress updating. Fortunately, there is another way to keep this pest from prompting you for your FTP user name and password.
Again, after the MYSQL login declarations in your wp-config.php file, add the following:
define("FTP_HOST", "localhost");
define("FTP_USER", "yourftpusername");
define("FTP_PASS", "yourftppassword");