Markelle Fultz speaks with Jeff Goodman about the prospects of playing for the Celtics and the "good and bad" from meeting with coach Brad Stevens. (2:09)

BOSTON -- Markelle Fultz, the potential No. 1 pick in the June 22 NBA draft, capped a two-day visit with the Celtics with an on-court workout Tuesday, then visited TD Garden, where he marveled at the championship banners and suggested he could envision himself trying to add to Boston's storied history.

"It almost feels like I belong here," Fultz told ESPN's Jeff Goodman during a tour of the arena that included a stop outside the Celtics' locker room, where the former Washington star studied the pictures of Boston legends that line the hallways.

The Celtics, Eastern Conference finalists after earning the top seed following a 53-win campaign, own the No. 1 pick thanks to the 2013 trade that sent Paul Pierce and Kevin Garnett to the Brooklyn Nets.

The Celtics already turned two previous first-round picks from the Nets into Jaylen Brown (No. 3 in 2016) and James Young (No. 17 in 2014). Boston had the right to swap spots with the Nets this season and own Brooklyn's pick outright for the 2018 draft.

Playfully asked if the Celtics had told him he'd be the No. 1 pick, Fultz said it never came up in conversation.

"No, no, no, they didn't say that. They didn't put that out there. I gotta earn everything," Fultz said. "Just talking to them, we didn't really talk about me getting drafted or anything like that, but more about me being a better young man, no matter where I go. Just what's going to make me the best player I can possibly be."

Fultz endured a series of medical tests and meetings with Celtics staffers on Monday before engaging in a solo workout at the team's practice facility on Tuesday morning. He capped his visit with a film session with Celtics coach Brad Stevens.

"My visit here was great. It was a good experience," Fultz said. "First of all, I came here, did some medical stuff at the doctors, a physical. I went out to eat later that night [with Celtics president of basketball operations Danny Ainge], that was a good experience just seeing the food culture here, got a good burger.

"Today, just being able to go up and have a blessed opportunity to play the game of basketball, first of all, then just working out for the Celtics, being able to work out, and show them what I have and at the end we did a nice little conditions test, the three-minute run, and just sitting down and watching game film, and film of myself, and how the team plays defense and offense and just learning more stuff about myself from film. Now, just coming to see the arena, and the city, it's just unbelievable."

Fultz told ESPN that he has not decided if he will work out for any other teams but, contrary to reports, he has not closed the door on the possibility.

ESPN Staff Writer Markelle Fultz stands outside the Celtics locker room. It's also Boston's war room on draft night and where they will phone in the No. 1 pick.

Ainge, who typically scoffs when asked for his opinion on how workouts went, didn't want to dissect how Fultz had performed in his solo session. So what was Ainge's biggest takeaway from his 24 hours with Fultz overall?

"He's talented," Ainge said. "I didn't find anything today that I didn't already know, which is the same case with almost every draft workout. ... He has a personality, has some charisma, he's fun."

One of the big questions for Boston is how Fultz would pair with All-Star point guard Isaiah Thomas. Fultz said he believes the two could thrive together, particularly with a bond as Washington products.

"I think me and him would be a great fit," Fultz said. "Just playing on and off the ball. He can go to 2, maybe I can go to 2. Being Huskies, we already got a connection. Being able to play together, we're going to motivate each other, we're going to help each other out. I think it would be something special."

Before he caught a flight home, ESPN led Fultz on a tour of the Garden. What would it be like for him to play there?

"I think it would be good if I come here." he said. "The fans here are great. I think that energy is just going to carry over to how I play on the court and just give me a little boost of energy."

When the frenzied atmosphere in the building during Boston's recent playoff run was noted, Fultz said he could tell just from watching.

"You can definitely hear it on TV, too," he said. "When I was watching and you can just see how excited everybody was and everything like that."

And what did he think of those banners?

"There's a lot," Fultz said with a smile. He joked how he used to play as Garnett, Pierce, Ray Allen and members of Boston's 2008 title team in the NBA 2K series as a kid.

Now there's a chance he could wear Allen's No. 20 next season.

"It almost feels like I belong here." Markelle Fultz on touring TD Garden

"I would want to wear No. 20, just because a lot of history behind that number, through high school and college," Fultz said. "[But] it doesn't really matter about the number; it matters about what I do."

Fultz praised the Celtics for their interest in molding him on and off the court. He said Ainge and Stevens talked extensively about how to grow as a person.

"It's crazy. I think it's a great organization," Fultz said. "They really care about you, on and off the court. They really just want the best for young men and people like me. They told me stuff I need to work on, they told me stuff that was good. I think that's the biggest thing, just helping me grow on and off the court, it's always what I've been about and I think that's special."

A photo of Fultz and Ainge appeared on social media on Monday night showing the pair dining at the b.good restaurant chain. Ainge, well known for his love of Chipotle, was asked why he hadn't brought Fultz to his favorite burrito joint.

"I had Chipotle for lunch," Ainge said with a laugh. And he quickly noted that the pair didn't want anything fancier.

"Fultz's flight was delayed [from D.C.] and he had a busy day and it was just quick," Ainge said. "We didn't want to go sit down at a fancy restaurant for two hours and have seven different courses in a meal. We wanted a quick bite, it was late at night."

Does a visit like the one Fultz had make it easier to decide what to do with the No. 1 pick?

"It helps us to get to know more [about the player]. Sometimes it makes [a final decision] harder, sometimes it makes it easier," said Ainge. "I don't know, we're not done. We're still in the process. We still have other players to see. Time will tell."