I don't think that's possible. However, you can log a particual PHP script file with something like xdebug.
What kind of VPS management interface (VPS technology) do you use. Virtuozzo for example has a very convenient Container's management tool.
In case of Windows VPS with Plesk control panel, we can easily find out such websites but in case of Linux it becomes quite difficult. For such issues in Linux VPS, we need to monitor the services using Top and MySQL database usage.