Believe it or not, something else could be wrong as well, not just necessarily the engine. While that could possibly be the case, I had an instance where my axle wasn't mating to my transmission securely because the axle seal on the transmission had lost the spring ring.

The MTF fluid was leaking out and flying back onto the exhaust, which of course burned it and smoke was coming up from underneath my car. When driving, it came out of the back, because of the wind, but when parked, it came out from the sides of the car.

So, moral of the story is, if you're familiar with what to look for underneath your car, I'd check everything to see if you have fluid dripping from someplace, and can visibly locate the point of origin.

If everything's dry and tip top, then you may want to have a trusted mechanic diagnose your engine for oil leakage of a sort.