Whirring noise

Most common cause for a whirring/buzzing type sound would be a wheel hub bearing starting to fail. Those will usually also change if you make turns while they are making noise. They sort of sound like mad bees. A bad bearing can make noise for months or it could fail tomorrow no real way to tell.

Next would be odd tire wear patterns. For those the sound would change depending on what the road surface is. Concrete/pavement/will sound different and it will stop on a dirt road.

If possible could you record a clip of it and upload it to this site? Hearing a noise can be real helpful in identifying it.

In that case it could still be a rear bearing but most will change with steering. Next would be engine related.
If you set in neutral with your foot off the clutch do you still hear it or is it gone?
How about holding the clutch in?
Now take it out for a drive. Get it up to the speed where it is loudest or you hear it good and push in the clutch and coast. Does the noise stay and slow down with the car or does it go away?
Being a manual those tests will help isolate if it is engine or transmission related. I would say to shut the engine off and coast but that can be an issue in some cars.
Have you driven it on different surfaces at all?
Did this noise just suddenly start or has it slowly gotten worse?