Here's another possibility (I had this problem once) -- maybe the water is condensate from the A/C.

The condensate is supposed to drain down two tubes (each on opposite sides of the transmission tunnel (under the medial kick panels, forward near the firewall) -- they're about 3/4 inch OD, and run down to the underside of the car.

Trouble is, they've got a filter (sort of like fiberglass) presumeably to keep insects from crawling up the tube, and this gets clogged with dirt from the air vents. The water, then, has no where to go but collect and eventually get splashed over the sides of the collecting tray and down onto the carpets on either side of the center of the dashboard. It can really soak the carpets -- I once made a sharp turn and the water just came over like a waterfall (alerting me to the problem) and soaked the pants leg of the person in the passenger seat. So it can well be your problem.

Good luck.