Following
@tabijan - suggestion - when you remove that coolant tanks cap - watch for those bubbles to rise up from that 3-way section of hose that is right by the thermostat and coolant outlet - there is another on the bottom side - but if the level in the clear tank drops quite a bit, it would explain the noise.
It also uses a "Burp line" that run across the top of the motor - from the rear side by the centerline where the rear bank of valves on the cover are - towards the front of the valve cover and over the injectors - running over across to the coolant tank - attaches thru a small port on the tank itself.
IF the coolant level is getting low - air and steam gets trapped in the back side of the rear section of the cylinder head where the exhaust valves reside - this is a very hot section as the hot exhaust doesn't have a place to go to shed it's heat when you're done driving - so if this seems to be the source of your noise, take a moment or two to let the engine idle to let the coolant flow back there and help take away some of that heat from back there- then just shut off the motor. It may help dissipate this noise - if letting it idle a few moments then the engine is shut off and it stops the gurgling - the issue is from the heat of that part of the cylinder head - not able to escape or get absorbed - it needs time to cool off
However, you own a Titanium - this may have a type of climate control system where the system "closes off" and moves the drum inside the climate control system once the system is not needed and you've shut off the ignition. It parks itself - you may be hearing the system park itself - this occurs after shutoff but not right at the shut off time - it takes several minutes to start and moves the vanes and drum for several moments - as it needs time to complete so you may be hearing the motors moving the drum and closing off the outside air port.
Depending on the system you have, Automatic - the one on the Left "Cycles" and can park itself to "Closed position" when you're parked and the ignition is off and it's not being used. The one on the Right is Manual and leaves itself where it's set at. But if you move the knob, with the ignition off it will cycle to "park itself" and the relocate to the new setting. But it may not be able to complete this until once the car is started again. Because; when the engine and ignition is off there is a timer on this length of time it can do this - so it will try to move to the new control setting - but it may not complete until the car is started again.