I'd suggest the first thing might be to remove the fan belt and run the engine for a short time to see if the noise disappears. There are a lot of things close by the water pump that could "phone" noise into it. Of course, don't run it more than a few seconds without the water pump turning. Likely suspects: belt tensioner or a pulley. while the belt is off, try spinning the pump by hand to listen for any noise, and wiggle the pulley to check for bearing play.

DG