Wiggle the fan blade and see if there is any play in the bearing. Do it with the fan belts loose and you'll be able to see the pulley's move. If the do for sure replace the pump.
If you don't have a clutch fan, or have play in the clutch of the fan on there now or if you have a big nut (which is left hand thread) consider replacing the pump with a 4 bolt pump and get a new fan/clutch combo. A Chevy truck clutch will bolt right on. I've been useing one for about 12 years and it works great.