There was the time, two seasons ago, when Eastern Europe's ambassadors for fluent football dismantled a talented Arsenal squad, in the spotlight glare of London to boot.
And any fan of Italian Serie A watches Kiev graduate Andriy Shevchenko shred the best defenders in the world on a weekly basis.
Even this year, striker Sergei Rebrov, also bequeathed from the famed Kiev academy, is being hailed as Spurs' key to European qualification at White Hart Lane in North London.
It all must represent a dizzying picture for Kovalenko to focus on.
"Yeah, I think about all that," Kovalenko, the 22-year-old midfielder for Major League Soccer's Chicago Fire, told me from his Chicago home via telephone on Thursday.
"But I've lived here (in America) for a long time now. I'm used to this life."
That existence includes being named a first-team All-American for 1998 national champion Indiana University as well as enjoying a regular starting position for what many neutrals view as MLS' most talented team.
The 5-foot-8, 145-pound midfielder (although he really is a jack-of-all-trades; "I even played right back this year," he said) was plucked from the hordes of young Ukrainian soccer-playing Soviets at the age of 10 and enrolled in storied club Dynamo Kiev's youth program for a five-year period.
"We were treated as professionally as the 21- and 22-year-olds were," Kovalenko said. "Every match was approached with the mindset that you were there to win. It was a very strict environment."
So strict, in fact, that stories circle the globe of Kiev's obsession with tactics and discipline. In European competition, a player was recently substituted for not being in prescribed place, even though the run of play resulted in a goal.
But, unlike, say, a freewheeling South American player who would decry such planned precision, Kovalenko credits that guidance when reflecting on his technically sound game.
"That's what carried me to this point," he said. "Being at Dynamo Kiev is what gave me the grounding to be the player I am today."
Kovalenko has followed Shevchenko's ascent in Italy with a keen eye. He recalls the affection the latter showed to him on a recent training trip back to Ukraine.
"We're only a year apart in age, and we scrimmaged together coming up through the system," Kovalenko said. "He came up to me when I was back there, asked me how I was doing."
If members of the Fire's brass were inquired on that front they would most likely respond quite well, thank you.
Kovalenko has raised the level of his game this year, tallying eight goals to accompany the bevy of assists that result from his pinpoint passing (he's right-footed, though, from watching him play you would answer ambidextrous if required to guess.)
On July 8 at Soldier Field, under the watchful gaze of his father Genady, in from Ukraine to watch his son play for the first time in four years, Kovalenko scored two goals, his first multi-goal professional start. "I was nervous. I respect my father so much," he said. "I love my dad, and it was nice to play for him like that. But you're only as good as your last game. I have to keep it going."
Kovalenko, who came to America at age 15 to live with a foster family, may soon be recapturing that form in Europe.
"I've had some calls recently," he revealed. "If someone makes a solid offer I'd go in a minute
"MLS is a terrific league, but it's hard not to want top play in front of 100,000 people (as Kiev regularly draw at home). That's what it's all about, really."
Kovalenko also finds himself facing the old dual-country FIFA litmus test: He's reaching a level of play at which he'll be asked to choose countries.
"I'm not an American citizen yet, but I want to be," he said. "But if Ukraine were to call me up for the national team, that's something I'd have to think about."
What requires no thought is absorbing the advice of Fire teammate Hristo Stoitchkov, the Bulgarian who once starred for Barcelona and lifted his country to unthinkable heights at USA '94.
"I don't think people (here) realize who he is," Kovalenko said. "He sits me down after matches, telling me what I should be doing better. I soak it all in. How could you not?"
If he bolts the American playing scene soon, Kovalenko will remember fondly his time at Indiana, an NCAA soccer factory that has produced Nick Garcia, teammate Yuri Lavrinenko and Aleksey Korol, among others.
"Not from the soccer side, but it's run better than most MLS clubs there," he said of his alma mater. "They even have their own plane."
But don't get the idea Kovalenko pines for days gone by. His Euro style fits in well with teammates Peter Nowak, Lubos Kubik and Stoitchkov, while that group complements the North American nuances of Chris Armas, Ante Razov, C.J. Brown and company.
"I think we have the best team in the league," Kovalenko said of the Fire, which hopes to recapture the form that led it to the American double -- MLS and U.S. Open Cup titles -- in 1998.
"Now, we just have to go out on the field and prove it."