The simplest and quickest solution would be to use the
<?php add_rewrite_endpoint( $name, $places ); ?>
So in your case it would be something like this:
add_rewrite_endpoint( 'user', EP_PERMALINK | EP_PAGES );
An user URL would look like this:
To access the variable:
$user = get_query_var( 'user', false );
HOPE so you find your answer!!