Gurgling noise when shifting the transmission into reverse?

Can you please shoot a quick video with your phone so I can hear the noise? That way I can tell for sure what's going on. You can upload it here with your response. It sounds like the coolant level can be low which will air bubble noises inside the heater core, please go over this guide which can tell you more:

https://www.2carpros.com/articles/vehicle-bubbling-noise

Please go over this guide and get back to us.

Ken, thanks for the fast response. I tried to get the car to make the noise again but had no luck. Will try again tomorrow, since it only makes it at first start up with transmission in gear, this case reverse. Your response makes sense of course, so I checked the radiator fluid, it might be a little low, but I will check again tomorrow and let you know. Thanks again, Ivan.

it could be a clogged transmission filter as well. If the noise is coming directly from the transmission, I would swap the filter on and install fresh fluid. Check out the images (below). Please let us know what happens.