sounds like its the evaporator drain, that is just water, and it will / it should do that anytime youre running or have been running the a/c or defroster.

 

Put a new hose on those fittings and get some quality hose clamps to hold it on tight. Heater hose breaks-down over time. From the inside ... especially at places where heat will form and cause the hose to lose it pliability and begin to deteriorate.

If this is a Heater hose ... lightly "Smear a thin coating" of waterproof grease on the Outside Diameters of the necks of the two places where that Hose fits. The waterproof grease will help get the hose on over the fitting and offer a degree of protection to having the new hose degrade at the fittings ... probably like the Old one did.