"This was a great team, a pretty good team, without adding myself and Carlos Boozer, and some of the key players that they added this offseason," said McGrady, who worked out for the Los Angeles Clippers last week.
"You bring a coach in like [Tom] Thibodeau, who's very defensive minded, very smart and knows the game, knows what to get out of his players.
"I think we can be really good, I really do."
McGrady, who also has expressed interest in joining Miami as a bench player in support of LeBron James, Dwyane Wade and Chris Bosh, said he wouldn't mind joining the Bulls in a reserve role, but his preference would be to start.
He also said he hasn't yet talked about a contract with the Bulls, but that was expected to take place at lunch Monday. McGrady is represented by Arn Tellem, who enjoys a very strong relationship with Bulls chairman Jerry Reinsdorf.
ESPN.com's Marc Stein reported that, according to a source, the Bulls are prepared to sign McGrady if he proves to be sufficiently healthy, and if he is willing to accept a bench role.
"I won't have a problem, but that's not what I'm really shooting for," he said of a potential reserve role. "I think, yeah, if I was the player that I was in a Knicks uniform, I would have no problem coming off the bench, but I've worked extremely hard and I'm far from being that player. Trust me."
The 31-year-old McGrady played in just 30 games last season as he recovered from microfracture surgery on his left knee.
"I feel good," McGrady said. "I've been battling to get back to rare form for two years, coming off of microfracture surgery, and it's been a tough road. But I feel pretty good compared to my last game I played in New York.
"I was still going through the rehab process, and I'm definitely a long ways away from what I used to look like. So I'm very, very confident in what I'm going to be coming up in this upcoming season."
Bulls All-Star Derrick Rose told ESPNChicago.com recently that he believes McGrady could help the Bulls.
"He's good," Rose said. "He's a player. If he just gives us half of what he's got, we'll be all right.
"But I know a player like him, he's going to go out there and give us his all, but he'll definitely help us if we get him on the team."
The respect is mutual.
"I'm very excited about the opportunity," McGrady said of playing with Rose. "If I do choose to come here, he'd definitely be the best point guard I've played with. The guy is very explosive. He's getting better every year. He's improving his jump shot. He's just a great young talent who has a tremendous upside to be a great player in this league."
McGrady thinks he would have no problem fitting in with the Bulls' young core.
"I fit in well," he said. "I just bring what I know about the game and my athleticism, and my versatility, knowing my smarts for the game, my leadership, just everything I can add to help these guys get over the edge.
"Without me, without Boozer, they're a .500 ballclub. And with the guys that they added, if they add me, I think we'll be 30 points better. I think we'll be a better defensive team with Thibodeau, who I played with for three years. So [the Bulls] have a really good chance of being good. The city should be excited about this team."
The Bulls courted McGrady as a free agent in 2000, but after much fanfare he decided to sign with his hometown Orlando Magic. Ten years later, the fact that he may end up in Chicago was not lost on him.
"It's a great city, sports town, great fan base, great team, first-class organization, what's not to like about playing for the Bulls?" he said. "I had the opportunity back in 2000, but I chose to go home. It's a full circle, here I am."
McGrady said he is not worried about the perception that he may not be a solid influence in the Chicago locker room.
"You can't worry about that," he said. "Again, Thibodeau was with me for three years, so if I was a bad locker room guy I don't think he would have had any interest in bringing me here, if I was that type of player.
"There comes a time when people like to say a lot of negative things about a player that's really not even true. I don't even worry about that, I go on. People know me. A lot of people around this league know me and know I'm not that type of person."
Nick Friedell covers the Bulls for ESPNChicago.com and ESPN 1000.