He moved to France a year later, but he was caught up in the general malaise that seems perpetually to hang over Paris St-Germain and, like so many Balkan playmakers, he never seemed to adapt to a more physical football culture. He drifted and was loaned out to Troyes, but resurrected his career and reputation at Rapid Vienna, which he helped to the Austrian Bundesliga title in 2008, before making the move to the MLS with D.C. United earlier this year.
These days the resemblance to Reeves is faded, and a small scar tugs at his right eye. I wondered whether there might be a sense of sadness about him, a feeling that perhaps he hadn't quite delivered on that immense talent, and I was half-expecting a lament about how it is football's loss that there is no place at the very highest level for his sort of languid talent. But he still seems as enthusiastic as he was in that Belgrade cafe in 2002, and the nearest he got to a complaint about skill being drowned out by physicality is an eye-rolling riff on officials in MLS during which he repeatedly pushed me to show exactly how much force is required (apparently far more than in Europe) before a U.S. referee will deem contact a foul.
He seems to be enjoying his time in MLS, even if his immediate (unsolicited) defense of it suggests some raucous dressing-room ribbing about his move there.
"A lot of people think the USA is not a good league," he said. "But it's a very hard league. Maybe tactically they are not as good as the teams from Europe, but they have a lot of Latin American players and they are physically good. Soccer needs a little more time to find a space, but with the national team at the World Cup people are more interested."
There is still a sense of gleeful disbelief about Boskovic at the direction football has taken him, which is understandable, for what is happening to Montenegro is a fairy-tale story to lift the most jaded of hearts. Montenegro became FIFA's 208th member three and a half years ago, and it started World Cup qualifying at the bottom of the pile, grouped alongside Andorra and San Marino in the lowest pool of European seeds. Since then it has risen to 40th in the rankings -- level with Colombia and above such established football nations as South Korea, Romania and Scotland -- and after beating Wales, Bulgaria and Switzerland (the last of those victories last Friday), qualification for the European Championship is within reach.
"Nobody expected this," Boskovic said. "We're a small country, we don't have a lot of players and we are new in this competition. After last year we have more experience, and in the last qualification we didn't have a lot of luck. Nobody thought we'd have nine points. We are happy and we deserve it."
Some context is required. The smallest nations to reach the finals of the European Championship are Slovenia and Latvia, both of which have populations of a little more than 2 million. Montenegro's population is 650,000. It is 20 times smaller than London. There were 12,000 at the City Stadium in Podgorica for the win over Switzerland, which may not sound like many, but to accommodate a similar proportion of the population, Wembley would need a capacity of one million.
Historically, Montenegro has been noted for its creators: Boskovic belongs in the tradition of Dejan Savicevic, Ante Mirocevic and Dragoljub Brnovic. The problem is that Montenegro's squad is packed with similarly creative players. Along with Boskovic, Stevan Jovetic and Simon Vukcevic both started out as classic playmakers, while Mirko Vucinic is very much a deep-lying striker. The problem faced first by former coach Zoran Filipovic and now by Zlatko Kranjcar is how to achieve a defensive solidity while still exploiting Montenegro's creative strength.
In World Cup qualifying, Montenegro tended to be either too defensive or too attacking, and so it flipped between dour draws and high-scoring thrillers. Experience, though, seems to have brought balance, and it has won 1-0 in all three games so far in Euro 2012 qualifying.
"We have a lot of good offensive players, but we also have good defensive players, players who can play any position in the defense," Boskovic said. "If you look how often we stop the opposition scoring, they really do a good job."
His role has changed as well. "When I started for Montenegro for a couple of games, I played where I played for my club," he said. "For the last three years at Rapid Vienna and now in the USA, I've played more in the middle. Now I play on the left side -- it's not my preferred position, but we've kept the team the same."
Vukcevic, similarly, has had to adapt to a role on the right while, in the absence of the injured Jovetic, Vucinic links the midfield and attack. He was sensational last Friday, a buzz of creativity and muscularity who ran the game and scored the only goal.
"He's a really important player," Boskovic said. "He can score from any position. I think when you watch last season in Roma as well, he's in the top-10 or maybe top-five forwards in the world at the moment. He's very good physically, technically. His character is strong and he has everything that you need."
Tuesday brings a tougher test as Montenegro travels to Wembley to face England. But as Savicevic, the former Red Star and AC Milan forward who is now president of the Montenegrin football federation, was excitedly explaining on Friday, even if Montenegro only beats Bulgaria at home and loses its other four remaining qualifiers, that will probably be enough to secure second in the group and a playoff spot.
Nobody expects Montenegro to finish ahead of England, and nobody expects it to beat England on Tuesday, which means the game is effectively a freebie. Anything Montenegro gets at Wembley is a bonus.
"We go without pressure," Boskovic said. "We aren't going there to lose, but everybody knows who England is. Beating Switzerland gives us a great chance."
And, improbably, it gives Boskovic the unanticipated hope of an appearance in a major tournament in the autumn of his career.
Jonathan Wilson is the author of Inverting the Pyramid; Behind the Curtain; Sunderland: A Club Transformed; and The Anatomy of England.