Considering that Tesla vigorously and publicly disagreed with Einstein on relativity in the 1930s, the answer is probably "no." Add to it that I've never seen any sort of actual citation for the quote in question, I am inclined to put it in the very large file of "stuff Einstein never said that people attribute to him anyway." Searching around the various books, databases, and articles I have, I see nothing that would suggest that this quote is legitimate. It is of course hard to prove that something did not happen, but in the absence of any indication that it did happen — I suspect it did not.
A few of the public Tesla references to relativity:
In 1934, on the occasion of his 79th birthday, Tesla denounced relativity theory as "a beggar wrapped in purple whom ignorant people take for a king" and "a mass of error and deceptive ideas violently opposed to the teachings of great men of science of the past and even to common sense... the theory wraps all these errors and fallacies and clothes them in magnificent mathematical garb which fascinates, dazzles and makes people blind to the underlying errors.... its exponents are very brilliant men, but they are metaphysicists rather than scientists. Not a single one of the relativity propositions has been proved." (NYT, 7/11/1935, p. 23).
He also claimed in 1932 that he had detected particles from the Sun that "vastly exceeded the speed of light," which would be contrary to special relativity. (NYT, Letter to the Editor from Bergen Davis, Columbia University, 2/24/1932)
Both of these are relatively (pun) late in Tesla's life, and early in Einstein's own fame (Einstein's world fame took off in 1919, picked up again when he fled Germany in 1933, and then became gigantic after the atomic bombs in 1945).
It seems, at a glance, to be a variant of this urban legend:
Jimi Hendrix was on the Tonight Show one time in the late 60s. Johnny Carson turned and asked him how it felt to be the greatest guitarist ever. Hendrix quickly responded: "I don't know. You'd have to ask Phil Keaggy."
While we can't say definitively that Einstein or Hendrix or any other publicly renowned great never said anything like that, that sort of question would be pretty peculiar to ask in an interview, it's not hard to imagine why somebody would make that sort of thing up. What better way to bolster the credibility of Phil Keaggy (and the Christian rock genre of which he was a progenitor) than a strong endorsement by Jimi Hendrix?
I can't find any instances of the Einstein version from before 2012. It would fit in nicely with the narrative of Tesla as an unrecognized genius whose legacy ought to be more widely acknowledged, popularized online by Cracked and the Oatmeal. While I can't say exactly what would motivate inventing such an anecdote, that seems likely.
I had it told to me as a joke by my friend who knows 1000s of yugoslav / bosnian / serbian jokes. it is typical yugoslav joke. It probably started like that then spread since the internet internationally. Tesla is god over there and it is appealing and funny to us from over there. Sounds even funnier in serbian / croatian / bosnian language/s. Perhaps it was even published in one of the satirical or comical papers or magazines in 60s-80s like Jez.