As far as I'm aware there is no musing in extant Graeco-Roman literature about a connection between dogs and wolves. There doesn't seem to be anything on this topic in Aelian's De Natura Animalium, for instance. Obviously, lacking a proper concept of evolution and indeed genetics more widely, it wouldn't really be possible to posit a 'biological' connection between the two species in our sense of the word.

There is some recognition that they are similar, at least in their looks: Columella says that shepherds should acquire white dogs as sheep-dogs, that they be less easily confused with wolves (De Re Rustica, 7.11.1). But what was probably the prevailing learned attitude towards dogs is given by Cicero who says (speaking through Balbus, the Stoic):

Think of the qualities of dogs: of their faithful guardianship, their fawning love for their masters, their hatred for strangers, their incredible keenness of smell in following trails, and their eagerness in the hunt – what else could it mean, but that they were made for the advantage of men?

(Canum vero tam fida custodia tamque amans dominorum adulatio tantumque odium in externos, et tam incredibilis ad investigandum sagacitas narium tanta alacritas in vevando quid significat aliud nisi se ad hominum commoditates esse generatos?)

(De Natura Deorum, 2.158).

i.e., dogs are provided for human use by the gods (or 'providence' more generally) - not much space in this conception for a descent from wolves.

It seems obvious to us now, but the establishment of dogs as descendants from wolves is in fact quite a recent development.

Nope. The Greeks and Romans knew that wolves and dogs could interbreed, but they also thought that dogs could also mate with other animals:

"...in Cyrene the wolf and the bitch will couple and breed; and the Laconian hound is a cross between the fox and the dog. They say that the Indian dog is a cross between the tiger and the bitch, not the first cross, but a cross in the third generation; for they say that the first cross is a savage creature" (Aristotle, On the Nature of Animals, 8.28)

Pliny the Elder also mentions that dogs could be crossed with both tigers and wolves, and adds that wolfdogs are especially common in Gaul, where

"their packs of hounds have, each of them, one of these [wolfdogs], which acts as their guide and leader. This dog they follow in the chase, and him they carefully obey; for these animals have even a notion of subordination among themselves." (Natural History 8.61)

This passage emphasizes the idea that dogs and wolves are essentially different, and we see this again and again when the two are discussed - as in Plato's Republic, in which dogs likened to philosophers, and wolves to tyrants. The dog is a friend to man (loyal, steadfast, etc.); the wolf is an enemy to humanity and livestock. It was thought, in fact, that the only other animal a wolf would tolerate was the parrot (or so the poet Oppian claims).

In mythology, there seems to be no conception of the relationship between wolves and dogs. Wolves were sometimes said to be descended from men who had consumed human flesh. Most famously, the cruel Arcadian king Lycaon was transformed into a wolf after feeding his son to Zeus (never a good idea in Greek myth). There was little speculation about the origins of dogs, though the dictionary of Pollux mentions the story that Molossian mastiffs were descended from an animated bronze dog Hephaestus made for Zeus.

More generally, the Greeks and Romans had a very vague sense of evolutionary biology. Several philosophical systems posited that all things were derived from a single principle (fire, water, or the like), and a number of philosophers (the earliest being the Presocratics Anaximander and Empedocles) speculated that mankind must have originated from other animals. But as so often in ancient science, theoretical brilliance was not combined with rigorous experimentation: there was no ancient Darwin who studied the anatomy of animals and theorized on the nature of the relationships between species. There was, moreover, an equally powerful philosophical tradition (epitomized by Plato and Aristotle) that emphasized the essential nature of every species.