I read this short story years ago on the net, and a lot of details have faded from my mind since then.
The premise is that there are these gigantic space-borne creatures that eats just about everything (but usually munches on asteroids) and as a consequence, accumulates a lot of rare and exotic elements in their bodies.
Their migration path just happens to intersect with a late 20th/early 21st century Earth. As a result, Earth's second contact is a bunch of alien tourists/scavengers chasing after the aforementioned space-whales looking to harvest their precious cargoes. Meanwhile, the space whales that landed on earth proceeded to act like giant kaijus that eats everything and gets treated like roaming natural disasters.
The protagonists of the story are a couple of these alien scavengers tracking the behemoths across the surface of Earth on locally bought/rented vehicles (I can't remember which) for the sake of expediency.