I had this problem in a tdi estate from new. The car went back to the dealership three times for 'rubber bungs' that apparently had come out, and undersealing (twice.) The rear footwell carpets were permanently damp. Eventually I sourced the problem by putting tissues into the heating ducts under the front seat. In a short time these were soaking wet - indicating an air-con problem. I confronted the dealer... 'Ah yes sir, the air con unit seems to have been faulty since new!' VW at first refused to replace the (now very soggy and smelly) rear footwell carpets - but keeled over pretty quickly.
Pour a bucket of water into the passenger footwell
it may be caused by the drain hole from the window screen being blocked it is located under the battery also check that the rain bar on top of the pollen filter is still there and not been left off allowing rain to travel in and down the heater pipes.
Rain
Heateer Core is gone
That's quite common situation. Under the bonnet are to holes (one is located under the battery) allowing water from engine bay to go out. When some dirt or leafs stuck there, water level goes up and water starts going through air vents to the car. Have it in 2 passats. Easy to fix with just a screwdriver. You must make those two holes open again.
If water is getting into the passenger footwell one or more of the weatherstripping has failed. Check the doors as the weatherstripping makes a funned to drain a lot of the water. If there is a leak that can be leading into the cabin of the car.
passanger side of water pump
Dry up the water. Take the car to a car wash and spray it good around doors and windows. If a leak is not visible then check the floor during rain storms while driving to see if water is coming in through a leak in the floor.
ruptured heater core
Get a bentley. Look it up.
Is it blood, oil, water, or urine?
Cracked heater core