The Wizards are said to be high on Jan Vesely and came away impressed with his athleticism during his individual workout. (Julio Cortez/Associated Press)

They could go with the mop-haired, trash-talking forward who left his homeland of Czech Republic four years ago to play in a basketball-crazed nation and beamed with pride as fans serenaded him after his last game for his team. Or they could go with shy big man from Lithuania who remains unsure about whether he will even play in the NBA next season as his agent attempts to negotiate a buyout agreement with his current team.

They could go with the confident forward from Turkey who is good friends with John Wall and spent an entire year as a practice player at Kentucky. Or they could go with the long-armed forward with the big hands from San Diego State. If all else fails, they could take the center from Texas who hopes to be in the analysts’ booth when his playing career is over.

The Washington Wizards could go a number of ways with the sixth pick in Thursday’s NBA draft, but the problem is they don’t know, and won’t know, what they will do until five other teams make their selections. Until then, Wizards President Ernie Grunfeld and other members of the basketball operations staff continue to finalize their draft board with the knowledge that they will either have to make a choice — or take whatever is left.

The primary focus for the Wizards going into the draft is coming out with more size. The past few weeks have helped make the options clearer for the Wizards, as they have had the opportunity to spend time with Jan Vesely of the Czech Republic and Turkish big man Enes Kanter during individual workouts and meetings; and they also sat down with Lithuanian forward Jonas Valanciunas during a trip to Treviso, Italy, earlier this month. All three said they could see themselves playing alongside Wall next season, but none was more adamant about his desire to play in Washington than Kanter, who reiterated that he’d be a Wizard if it were up to him.

“I would love to go to D.C.,” Kanter said on Wednesday from a ballroom in a Times Square hotel where the top 15 draft prospects met with reporters. “It’s an international city. Obama loves basketball. I would love to play with John Wall.”

But Kanter could easily be taken third by Utah, or fourth by Cleveland, which is also believed to think highly of Valanciunas at that spot. Many scouts rate the 19-year-old Valanciunas as the international player with the most upside in this draft, but lottery teams might have a hard time trying to justify selecting a player whose buyout agreement reportedly could keep him from playing in the NBA until 2012. But a source with knowledge of the Wizards’ thinking said on Wednesday that waiting on Valanciunas “might be worth it.” Valanciunas was optimistic that a buyout agreement allowing him to play next season could be reached with his team, Lietuvas Rytas, but estimated that it would cost $2.5 million.

NBA teams can only pay $500,000 toward a buyout, which would place the remaining burden on Valanciunas. “It’s really tough. Lietuvas Rytas don’t want to let me out. I believe my agent [Leon Rose] will fix this problem,” he said. “I just want to get to the NBA and begin playing.”

If Valanciunas is still around at No. 6, it could create a predicament for the Wizards, who are also very high on Vesely, according to multiple sources, and came away impressed with his athleticism during his individual workout on Sunday.

Nicknamed “the Flying Czech” for his acrobatic dunks, the 6-foot-11 Vesely has been compared to Utah Jazz forward Andrei Kirilenko and is the most experienced of the international trio. He spent the past few seasons with the Partizan Belgrade in Serbia. He claims that the pressures of playing for some of the most intense fans in Europe contributed to him shooting just 44 percent from the foul line last season, but he felt rewarded when he scored 18 points to lead his team to the Serbian title and fans chanted his name for several minutes.

“I liked that,” Vesely said. “I learned a lot about basketball and about life when I was there.”

The Wizards will look to Texas freshman Tristan Thompson or San Diego State swingman Kawhi Leonard if one of their three primary targets is off the board. The 6-8 Thompson said his workout with Washington went well, “then again, nobody tells you that you had a bad workout. We’ll see how it turns out.”

Leonard could provide a fallback perimeter defender for the Wizards and give the team a dimension that it currently lacks. “Defense. I pride myself on that, every night, giving my full effort,” Leonard said, adding that he is ready to take on the likes of LeBron James. “I still got improvements to make. But right now, I’m not afraid of anybody on the court. I’m a competitor.”