2005 Corolla Noise at low speed

Hi all, first post. I own a 2005 Toyota Corolla. Superb machine. Except that at low speeds or idle, there is frequently a high pitched whine, or whistle like sound especilly when I gently tap the accelerator pedal. Will also occur occasionally when downshifting (automatic transmission) to low speeds. Seems mostly to occur in "Drive". The dealer checked the car out and couldn't locate the source of the noise. They advised that it "definitely is not drive train". I realize that there is a warranty on the power train, but the noise is annoying and could cause me difficulties if I choose to sell.

Anyone out there with a similar problem? Any suggestions? Appreciate any feedback.