A species is defined by one simple thing: if individuals can interbreed and produce fertile offspring. There are complications related to ring species and few others, but they're not applicable here.
All human beings from all over the world can interbreed and their children will be fertile themselves (with the same rate of accidental infertility they would find in their own populations). As such, it would be completely preposterous to claim that there is more than one species of human on the planet today.
There is actually a substantial debate on whether wolves and dogs are the same species or separate, precisely because they produce fertile offspring so easily. While wolves are firmly identified as Canis lupus, you can find modern sources calling dogs both Canis familiaris (a separate species), and Canis lupus familiaris (a subspecies of wolf).
Probably the better example you could give is bears, where brown and polar bears are always considered separate species, but they do successfully interbreed, even in the wild occasionally.
The species concept is a little too vague, and essentially the difference between two closely related species and two distant varieties of the same species is fuzzy and often historically biased (if the two populations were considered separate species for a long time, there is large inertia against re-categorizing them as a single species when evidence of genetic similarity and interbreeding arises).
The definitional limit on interbreeding includes geography and preference; black/brown/polar bears can and do interbreed in captivity but because they live in different locations and they look sufficiently different/have different diets we consider them different species.
If Aliens landed on our earth 20k years ago and used our definition of the word there's no doubt in my mind they'd consider us different species, we'd be like bears. As far as I can tell the only reason we don't classify people as different species is for the sake of society, as people would naturally then try to determine differences and rank them, which has an obviously bad long-term outcome.
There are much better arguments that brown/polar/black bears should be considered a single species, and that they perhaps would be if they were first discovered today. It is true that the distinction between "two closely related species that diverged recently" and "two distantly related varieties of the same species that are diverging more and more" is quite vague and subjective - especially when there are large phenotypic differences.
However, few of these arguments apply to human populations. With the exception of dogs, cats and other domesticated animals, few or no other mammal populations that have diverged as recently as humans are categorized as separate species (for example, brown and polar bears have diverged ~600k years ago, before our species even existed). Human populations only began spreading out of Africa some 150k years ago, which is not a lot of time in evolutionary terms at all, for a mammal that only reproduces around 1/year and needs more than a decade between generations.
Not to mention, the separation between all human populations is merely geographical. When different human populations came into contact, even ones that had been isolated from each other for tens of thousands of years, they virtually always interbreeded in significant numbers, contrary to, say, wolf and dog populations. This is also a strong argument against considering distant human cousins different species.
Additionally, morphological variation among isolated human populations is actually quite small, compared to intra-population variation. Skin color is the single biggest morphological difference, by far; followed by the size/hardness of our hairs, especially the ones on the head. Apart from these, virtually all other differences are more about statistical prevalence of certain traits (e.g. blue eyes are more or less common in various populations, body hairyness is more common in some populations than others, tallness is more common, etc).
All human beings from all over the world can interbreed and their children will be fertile themselves (with the same rate of accidental infertility they would find in their own populations). As such, it would be completely preposterous to claim that there is more than one species of human on the planet today.