I don't think I fully understand.
The noise only happens when the car is moving forward, but it does not change in volume or pitch with road speed or engine speed?
What about when you turn the steering wheel?
The first thing that comes to mind is a hydraulic pump, but that would make noise whenever the car is running, whether it is moving or not, and would change pitch with engine speed. If it turns out to be the hydraulic pump in the power steering, many of us have been able to quiet those down with fresh fluid. It is a good idea to pull out the reservoir and clean the screen as well. You you are going to pull out the reservoir, you may as well replace the power steering hoses. They are probably leaking anyway, right?