You did not say what you are working on, YEAR AND ENGINE SIZE.
But in most cases or designs the water pump can not leak oil into the coolant. The water pump has nothing to do with the engine oil.
Does the engine have a engine oil cooler on it ? That would be 2 oil lines just above the oil filter that runs down the side of the engine oil pan a go to the radiator. There are tubes inside of the radiator that oil flows through and they are none to leak oil into the engine coolant that's inside of the RADIATOR. If they are leaking then REPLACE RADIATOR. BUT like I said I don't know what you are working on.
Would like to help you with your problem, But need more INFO. NEUTZ.
If it is a water-filled or oil-filled radiator, it will leak fluid.
It would be possible to cause an oil leak while replacing the water pump.
Water pump or bad hose clamp
There might be a leak in the water pump, or in the radiator. Maybe even check the radiator hoses for cracks and leaks.
You have a blown headgasket or cracked cylinder head/engine block. It can also be a leak at the oil cooler. Its at the oil filter mounting, check that 1st.
There could be a leak, maybe a small leak, and only when it overheats. Also, check the oil and make sure there is no water in the oil. It will probably look weirdly milky on the dipstick if there is water in the oil.
You have a leak and a large one. If you or a cheap store just changed oil, then they may not have attached the Oil Filter or the Oil Pan Plug correctly. If you leave off an O-ring or don't lube the gasket on the oil filter, then it could leak. Generally this will not leak very fast. The oil pan plug is at the bottom of the oil system and it would leak out all of the oil. Check your radiator water. Sometimes an engline will leak oil into the coolant system and it will be carried to your radiator. This will turn the water a chocolate milk color.
if you are getting water in your oil its eather a busted hear or head gasket if no water in oil it could be water pump
there could be a leak in the oil cooler or maybe a head gasket or a cracked block. Is there every any water in the oil?
they leak oil from the oil pump on the front of the engine
Coolant system leak, faulty thermostat, lack of (or long overdue change of) engine oil... low fluid or bad thermostat, low oil, bad radiator,clogged water pump. You should also make sure that the radiator and a/c fans are working propperly
No, it causes a massive coolantleak.