Yep, assuming by background it's just any backdrop like a plane or something.
In the scene tab, just drag and drop the background onto the camera. Now whenever you move the camera (even when used in the viewport) the background will also move.
You can do this for any object in the scene not just background and remain in the same position relative to the camera.
View attachment 1282479
View attachment 1282481
This means, from the cameras perspective, it will always show the same position of the background