WP asking for ftp pasword on VPS server

The short version is that PHP is probably running under the incorrect user. The following thread discusses this issue, and options for resolving the problem:

https://www.ads-software.com/support/topic/plugin-install-asks-for-ftp-details?replies=8

Thanks for the reply!

Usually when you see this kind of issue, it is because the WordPress directory is owned by an user other than the user which the web server is running as.
You would just need to run the chwon command in the format below.
chown -R ownername:groupname path/to/wordpress/

Example
chown -R www-data:www-data /var/www/html/wordpress