If the whining sound goes up in volume with rpm, could be water pump bearings, so inspect the water pump for any leakage, if possible, but it would be hard to see.
When water gets into bearings, it washes out the grease, and will also start to drip from the weep hole, it's a sure sign the water pump is on it's way out. Another easier to spot sign would be white oxidation on or around the pump itself. Other than that, could be alternator bearings.
If the seller agrees, you can just untighten the belt using the screw on the alternator, and check both of them for any play in bearings, or any weird sound, few minutes work.