Fran Fraschilla explains what makes Markelle Fultz such a good teammate and why he should be the No. 1 overall pick. (0:45)

Washington point guard Markelle Fultz, the potential No. 1 pick of the NBA draft, said Tuesday that he has had multiple conversations with Boston Celtics president of basketball operations Danny Ainge since the draft combine earlier this month and that he is hopeful he will be selected first overall on June 22.

"I've talked to Danny a few times, and they want to get me to come out there for a visit," Fultz told ESPN. "They just want to get a chance to know me better as a person."

"I want to be the No. 1 pick really bad," Fultz added. "It's been a dream of mine since I was a little kid, and I feel like I would fit well in Boston."

Fultz said he has yet to firm up a day when he will visit the Celtics, who acquired the rights to the No. 1 pick through a 2013 trade with the Brooklyn Nets. He will likely work out for management and coaches. He did meet with Boston and a few other teams earlier this month while in Chicago before the draft combine.

"I want to be the No. 1 pick really bad. It's been a dream of mine since I was a little kid, and I feel like I would fit well in Boston." Markelle Fultz

The 6-foot-4, 195-pound Washington, D.C., native averaged 23.2 points, 5.9 assists and 5.7 rebounds per game as a freshman at Washington this season while shooting 41 percent from beyond the arc. Multiple sources told ESPN that Fultz is the front-runner to be selected first overall.

Fultz said he has never been to Boston, but he has watched the Celtics closely through their postseason run that ended last week in the Eastern Conference finals.

"I don't know a ton about the city," Fultz said. "I know the tradition the franchise has, and that the fans are crazy."

Fultz has developed a relationship with Celtics All-Star Isaiah Thomas, who also attended the University of Washington. He said the pair met on his recruiting visits and have stayed in touch since. Thomas, also a point guard, is coming off a career season and has one year left on his contract.

"We can both play on or off the ball," Fultz said. "We can both score and also pass. I think we'd be great together. When we've talked since the lottery, we haven't really talked about basketball much. He's been through a lot lately."

Fultz is aware that he is somewhat of an unknown heading into the draft because he played for a Washington team that won just nine games this past season.

"I'm a versatile point guard who is unselfish and can score at all three levels," he said. "I can rebound, block shots, push the ball, basically anything you need from a guard. Off the court, I'm humble."