Anthony and his wife, LaLa Vazquez, are from the area.
"That's like the ultimate dream at the end of the day," Anthony said. "Who wouldn't want to go back home to play?"
"I don't know, I mean I can't really answer that question," Anthony said when asked where he wants to play next season. "It's tough for me to sit here and say, 'Oh, I want to play in New York' [or] 'Oh, I want to play in New Jersey' [or] 'Oh, I want to stay here in Denver.' "
Anthony admitted he's had a difficult time dealing with all of the trade rumors.
"It's kind of hard for me to even watch sports right now," Anthony said. "That's all they're talking about right now."
He added, "I haven't had a good night's sleep since Thanksgiving."
Anthony said he was surprised when the Nets emerged as possible trade partners with the Nuggets.
"I [had] never really thought about the New Jersey Nets," he said, before allowing that he has subsequently considered the possibility.
"I see what the future holds, they'll move into Brooklyn. ... Me going back home to Brooklyn, opening that arena ... I think about all that stuff."
But Anthony also said, "I haven't even thought about [signing an extension with the Nets]."
If the Nets do trade for Anthony, they would likely want assurances he would sign the three-year, $65 million extension he left on the table with the Nuggets. If not, he would become a free agent after the season.
Anthony refused to say he would sign an extension with another team, saying "I have to weigh everything, all the options."
On Saturday before the Nuggets' home game versus Cleveland, Anthony clarified his conditions for signing the extension.
"I got to feel like I have a chance of reaching my ultimate goal of a championship," Anthony said. "Going to a bigger market is cool, but if I feel like I have a chance of winning a championship here in Denver in the next five years, then I'd sign the extension."
As for speculation his preference is to play for the Knicks, Anthony said during the ESPN interview that the assumption originated from last season when the Nuggets were playing at Madison Square Garden and he said:
"Who wouldn't love to play in one of the greatest arenas in the world?"
He also believes the Knicks speculation was fueled in part by events at his wedding in New York this summer.
"It got out the next day that me and [New Orleans Hornets guard] Chris Paul were supposed to be in New York," Anthony said of the infamous toast that Paul reportedly made, but Anthony downplayed it, saying it was all in jest.
"It was a lot of laughter, a lot of joking, no one took it serious."
Anthony described himself as being in a "lose-lose situation." He said no matter where he chooses to play, he'll disappoint the fans of a team he doesn't choose.
Anthony said while he's been able to stay focused on basketball, he's aware of the magnitude of the looming decision.
"Any decision I make is the biggest decision of my life," Anthony said. "It'll carry on and it'll follow me for the rest of my life, too."
"[This decision] will define my legacy."
He did say he won't emulate LeBron James' process, in which the former Cleveland Cavaliers star announced on "The Decision" on ESPN he was taking his talents to South Beach to play for the Miami Heat.
"I will not do it that way," Anthony said, before adding "as far as his decision, I support him, that's one of my close friends."
Anthony took exception to the idea he wanted out of Denver, disagreeing with that characterization. He says he holds Denver in high regard and cares about Nuggets fans.
"I was able to step right in and live up to the expectations," Anthony said of joining the Nuggets after one year at Syracuse.
Denver won 17 games in 2002-03, but in 2003-04, his rookie year, Anthony led the Nuggets to the playoffs, and they've been in the postseason every season since.
Anthony thinks he'll be traded before the deadline if he doesn't sign the extension with the Nuggets.
The most recent trade talks have Chauncey Billups and former Detroit teammate Richard Hamilton reuniting in New Jersey along with Anthony in a megadeal that includes three teams and more than a dozen players.
Anthony has said he feels remorseful that Billups has come up in the talks, knowing the Denver native wants to retire with the Nuggets. He chats with Billups all the time about bringing a title to Denver.
The Nuggets reached the Western Conference finals in 2009, only to be beaten by the Los Angeles Lakers.
Last season, Denver was knocked out in the first round by Utah, a frustrating end to a tumultuous year in which coach George Karl battled throat and neck cancer.
"That's something we always talk about, bring a championship back here. I don't just go out and play basketball just to do it. That's on my mind," Anthony said Saturday. "That was my dream."
Was his dream?
"If I feel I can't do it here, I don't think this is the right thing to do," Anthony said. "It's just the uncertainty in the future of the organization. It's a lot of things that come into play, contracts, not knowing what's going to happen in the future."
Anthony said in the ESPN interview he is concerned about the expiring collective bargaining agreement and the effect it could have on his financial stability.
He said the new CBA is "the most important thing right now" as he weighs his future options. He would risk losing millions of dollars by entering free agency under a new agreement, which is likely to have a lower ceiling for player salaries.
Ultimately, Anthony said playing for a winner is more important than money.
"That gold ball is what everybody wants," he said of the NBA Finals championship trophy.
Information from The Associated Press was used in this report.