Are you sure the whining is coming from the engine and not from the stereo speakers?
Interference from the alternator can cause a whining noise through the speakers when the radio is on.

You can check this by, erm, turning the radio off.

Usually wise during a test drive anyway.

Does the whine alter when you rev the engine up or when the actual road-speed increases?

If it alters with engine it could be belts or the alternator or a/c pump

(assuming it's not actually a knackered engine).

If it alters with road speed it might be something as simple as a tyre catching on something or something as dodgy as a knackered gearbox.

Unless the owner could show me what the whine is I'd probably walk away.
