I have the same vehicle. That's the thermostat housing. Hopefully, the leak is either the upper radiator hose, or the thermostat housing seal. I flushed my cooling system last year and it was very easy.
Here's some info I posted in another forum:
Cooling System Flush. 2002 Escape 2.0L 5MT:
Motorcraft Premium Engine Coolant (Green)
System capacity is 5.3 qts (50/50 mix of coolant & distilled water).
Radiator drain valve: 19mm socket or wrench
Radiator drain valve tubing: ~9mm ID or ~3/8" ID
(for collecting the coolant more easily - I routed the tubing out towards the front of the vehicle into a bucket).
Radiator upper nipple: ~37mm OD (this should be the same as the radiator hose ID).
Engine block coolant drain plug: T40 Torx wrench (I didn't remove it).
Thermostat housing screws: T25 Torx wrench. 89-Inch/lbs (do not overtighten - the housing is plastic)
Temporarily remove the thermostat so that the sytem can be flushed.
When done with the flush, reinstall the thermostat w a new seal.
(replace the thermostat if necessary; mine was fine, so I didn't replace it).
Using a shop vac hose & etc, I fabbed a water hose setup & connected it to the upper radiator nipple to flush the cooling system. I also rigged a swimming pool hose to the radiator/thermostat-housing hose so that the old coolant could be collected more effectively & so that the clean flush water could be directed to the lawn.
I used two 2.5 gal jugs of distilled water as a final rinse.
Note: I did not remove the engine block drain plug. It may not be necessary on the I4, because afterwards I was able to add the correct amount of coolant & distilled water.