You cannot preselect a Project Manager in a Project Request, however, there is an alternative.
If you want the Project Requests to list whom should be the PM for a project you can create a custom field (such as a text field or a pick list) to add to a Project Request Type.
This will give people the option to list who they will want to be a PM.
It is good to note that this will not preclude selecting a PM when generating a Project from a Project Request. That action will still have to take place.