Marco Polo is a very tricky figure.

If Polo was referring to something real in China in the 14th century that was dragon like, he possibly was referring to Chinese Alligators. Chinese alligators are Alligator sinensis, the other species in the genus besides the American Alligator, Alligator mississippiensis. Chinese alligators are quite a bit smaller than their American cousins, and historically their range was restricted to the Yangtze River valley. Because of habitat loss (the type of wetlands they live in tend to get used for rice agriculture) it is critically endangered, with some 300 left in the wild.

Polo's description is as follows from Chapter XL of the Thomas Wright translation ("On the province of Karazan"):

"Here are seen huge serpents, ten paces in length, and ten spans in the girt of the body. At the fore−part, near the head, they have two short legs, having three claws like those of a tiger, with eyes larger than a fourpenny loaf (pane da quattro denari) and very glaring. The jaws are wide enough to swallow a man, the teeth are large and sharp, and their whole appearance is so formidable, that neither man, nor any kind of animal, can approach them without terror."

Polo then mentions how these "serpents" live in caverns, and drag themselves to bodies of water ("to drink"). Polo then gives a very detailed account of how they were supposedly hunted, the medicinal uses of its gall bladder, how highly esteemed the meat was, and then...moves on to horses. No mention of pets that I see.

Also interestingly at least in this translation they're not specifically called dragons either: when the term is used it's in reference to the creature in Chinese art and the Zodiac. Wright (and other historians) seem pretty convinced that this description here is of the Chinese alligator, however.

But I should caution that we can't really be sure exactly that Polo is referring to a local wildlife species because Polo not only was rather infamous for his exaggerations (such as claiming Hanzhou had 12,000 bridges, unlike it's actual 350 or so), but because as a Medieval European he also plugged in mythical animal tropes to his accounts. And when I say "he" I should clarify it's really a "they" - while the Travels of Marco Polo might have been based on manuscripts and travel logs written by Polo, this work isn't the latter thing - it uses such supposed sources to write the travel book, and Polo worked closely with romance writer Rustichello da Pisa to write the Travels. Occasionally the narrative flips from the first person to the third person, even, and Rustichello absolutely spiced up the narrative, adding mentions of men with tails in Sumatra and men with the heads of dogs in the Andamans. Stories of dog headed people (in India) date back to Ancient Greek writers and are a very old trope.

For more on the Travels manuscript, you should check out this answer by u/sunagainstgold, and this answer by u/The_JackMeister on its general reliability.