This is what a friend of mine that's a Whirlpool repair man says...
It is always hard to tell when listing to a recording or even over the phone, but I would guess that something is in the water pump. It may go away? I would just keep using the machine unless it brothers him a lot.
On that note, I have pulled stuff out of the water pump on various machines with relative ease. Usually you take the front panel off the machine, and the pump is right there.
On some models it does. I remember a former roommate once chewed me out because I "broke" the washer. It was making an objectionable noise after I had used it. When I took the front panel of the machine off, I found the noise was coming from the water pump. When I took it off, I pulled the underwire from a bra out of the pump.