What permission are required to select an existing event location in CiviEvent?
If you're able edit an event, I don't think you need any additional permission to add existing location for an event. 

The reason why you don't see an option could be because you haven't yet created any event location on this site? If this is the case, try adding a location for this event and then create a second event - you must be able to choose location on this newly created event.