There are a lot of posts around about the FTP prompt when preparing an upgrade and all (almost all) reference the same information which is to enter specific settings in the wp-config.php file for the FTP site, username, & password.

Alternatively, I prefer this option which allows the admin user with the correct permissions to avoid the FTP aspect altogether.

In the same wp-config.php file in the WordPress root, around line 10 it will look like this:

[php]
* This file is used by the wp-config.php creation script during the
* installation. You don’t have to use the web site, you can just copy this file
* to "wp-config.php" and fill in the values.
*
* @package WordPress
*/

// ** MySQL settings – You can get this info from your web host ** //
[/php]

Just insert a few lines and add the 3 DEFINE lines as per the example below:

[php]
* This file is used by the wp-config.php creation script during the
* installation. You don’t have to use the web site, you can just copy this file
* to "wp-config.php" and fill in the values.
*
* @package WordPress
*/
define(‘FS_METHOD’, ‘direct’);
define( ‘FS_CHMOD_DIR’, 0775 ); // change these settings to match your apache account
define( ‘FS_CHMOD_FILE’, 0664 ); // change these settings to match your apache account

// ** MySQL settings – You can get this info from your web host ** //
[/php]

The key is the CHMOD entries. In my case the cpanel / WHM server is configured for the apache account to act as the group controller of the files. So to upload and modify files in the Worpress directory it needs write permissions as group not owner.