According to one Knicks player Carmelo Anthony spoke to recently, he gave no indication he was planning an exit strategy from New York.

The source told The Post this week one reason Anthony wants to remain in New York is he has enjoyed being in a big media market, as opposed to being in Denver.

The Post reported two weeks ago Knicks officials liked their odds of re-signing Anthony following their June 13 dinner meeting in Los Angeles in which Phil Jackson, coach Derek Fisher and general manager Steve Mills met with Anthony and his agent Leon Rose and broached the Mavericks trade.

The Post reported the organization likes its chances because of cap-space issues of Chicago and Houston. ESPN.com confirmed The Post report Saturday, saying Knicks officials were “increasingly optimistic’’ about their chances because Anthony and Jackson have “connected.’’ And now Anthony has a more consistent point guard in Jose Calderon, one of seven players Jackson added this week.

In Anthony’s words, nothing is official until a deal is “signed, sealed and delivered,” and Tuesday he dips his toe into the free-agent waters for the first time in his NBA career — something he has said since October he wanted to experience.

Anthony has planned visits to Chicago, Houston, Dallas and Los Angeles, where he has an apartment and the Lakers have cap space. There’s no plans on visiting Miami yet, but Heat president Pat Riley has called the Big Four scenario a “pipe dream” — even though of the current Big Three, LeBron James and Dwyane Wade have opted out, and reportedly Chris Bosh will do the same.

The Melo Drama began in October when a New York Observer story quoted Anthony as saying, “I want to be a free agent. I think everybody in the NBA dreams to be a free agent at least one time in their career. It’s like you have an evaluation period. I want to experience it.’’

The next day, Anthony became defensive about the article’s perception.

“Does that mean I’m not coming back to New York?,’’ he said. “Not at all. But it’s definitely an opportunity I’m willing to explore and experience. That not whatsoever means I’m not coming back to New York or I don’t want to be in New York.’’

A lot has happened since — the Knicks going from 54-28 to a 37-45 disaster.

“He is stepping into a situation in which people are going to appeal to him and his better self and about what their team is, and he is going to have to make that judgment call,” Jackson said Thursday.

Anthony has talked about wanting to be on a title contender, but his most recent comments have indicated the Knicks are the favorites. He acknowledged his pow-wow with Jackson, Fisher and Mills was “a great meeting’’ and said of Fisher’s hiring, “I like everything Phil is doing.’’

In a recent video, Anthony said he’s worried about uprooting his 7-year-old son Kiyan and is looking at the “big picture’’ of six years, not his title chances next season. Rose said Monday, “Carmelo loves being a Knick, he loves the city and the fans.’’

And yet the Bulls still pose a threat, even if their cap situation is more complicated than quantum physics. CAA’s William Wesley is an advisor for both Anthony and Bulls coach Tom Thibodeau. The Bulls still have cap work to do and need to convince Anthony they’re not gutting the team. Their best hope is convincing Jackson to work a sign-and-trade.

The Bulls’ draft-night trade for shooter Doug McDermott gives them the ability to dump Mike Dunleavy’s contract, amnesty Carlos Boozer and offer Anthony close to $17 million for four years. They do not want to sacrifice Taj Gibson.

Anthony can make a starting salary of $22.5 million over five years in New York, though if he re-signs he likely will take less to give Jackson flexibility in 2015. If Anthony demands the full max from Jackson, that could lead to issues.

In need of bigs, the Knicks have the $3.27 million mini mid-level exception for a free agent and would love to sign Jackson favorite Pau Gasol, with a big discount. But a more likely scenario is signing Gasol’s Lakers teammate, power forward Jordan Hill, a former Knicks first-rounder, or Kris Humphries.

The Knicks have other free agents in center Cole Aldrich, Shannon Brown, injury-prone Kenyon Martin and point guard Tour’e Murry, whom the Knicks have until Monday to offer a $1 million qualifying offer to make him restricted. Only Murry has a shot at returning.

Destination unknown

Here’s a look at possible landing spots for Knicks free agent Carmelo Anthony:

Bulls

Pros: Chicago more prepared than Knicks to compete for East crown if PG Derrick Rose is healthy. Anthony has great respect for coach Tom Thibodeau. Big market. Sign-and-trade could mean they can offer close to the max. Assuming Melo paycut, possible to have roster that includes Anthony, Rose, Taj Gibson, rookie Doug McDermott, Jimmy Butler and coveted 6-foot-10 European prospect, forward Nikola Mirotic.

Cons: Is Rose the next Amar’e Stoudemire? Bulls may have to gut the team too significantly to give Anthony a salary close to $20 million.

Skinny: Best bet is if, deep down, Phil Jackson doesn’t want Anthony and works a sign-and-trade, feeling he can lose him elsewhere for no compensation.

Odds: 7-2.

Rockets

Pros: Are on their way to clearing necessary cap space — Omer Asik already shipped and GM Daryl Morey reportedly has a deal in place to send off Jeremy Lin. Possible Big Three of Dwight Howard, James Harden and Anthony. No state income tax in Texas.

Cons: A big TV market, but celebrity cachet goes away. Western Conference is so rugged, he may be no closer to The Finals.

Skinny: Howard’s recruiting powers will be a test. Already lobbying the Melo Brand won’t suffer in Texas.

Odds: 5-1

Mavericks

Pros: With Dirk Nowitzki expected to take his usual free-agent discount, Mavs will have maximum cap space. Possibility Mavs also could land LeBron James. Former Knicks mate Tyson Chandler now in Dallas. No state income tax. Owner Mark Cuban one of the best.

Cons: If James not in mix, Anthony and Nowitzki might be too redundant — big scorers but very average defenders. Melo can never be bigger than the Cowboys.

Skinny: Anthony could threaten Jackson that he’s ready to go to Big D for no compensation if he doesn’t sign-and-trade with Bulls.

Odds: 8-1

Lakers

Pros: Already has home in L.A. Coaching nemesis Mike D’Antoni is gone. The Anthonys and Bryants are friends. And it’s hard to say no to Kobe if he makes a big pitch. They have cap space for max contract. Drafting of Julius Randle makes it even more attractive despite coach-less state.

Cons: Why would Lakers president Jeanie Buss humiliate her fiancée, Jackson. Signals are organization has no interest in a Bryant-Melo duo.

Skinny: Probably more Hollywood fantasy than reality.

Odds: 10-1

Heat

Pros: The idea of creating a Beatles-like Big Four, though Miami president Pat Riley but he’s called it “a pipe dream’’ — but so was original Big Three idea. All four opt out and sign one-year deals. Or Chris Bosh goes to his hometown Dallas to open up a slot for Anthony. No state income tax.

Cons: Does Anthony want to leave as much as $70 million on the table? Will he get credit as a champion if Miami wins title, considering his cast? Heat still have no interior.

Skinny: New commish Adam Silver might sign up for it sooner than Anthony.

Odds: 12-1.

Knicks

Pros: Stay in Big Apple. There is cap room in 2015. Tiangle offense could be made for him. Now has a playmaking point guard in Jose Calderon. Signing elsewhere would leave his New York legacy as a giant disappointment. Why would he give up on the Zen Master?

Cons: Jackson is selling the 2015-16 free-agent bonanza, though a different regime aimed for the same, and failed, in 2010. There’s a 41-year title drought that suggests the franchise is forever jinxed or haunted by owner James Dolan’s corporate culture.

Skinny: Fans who think Knicks better off if Anthony leaves are forgetting, there’s only a small handful of players as dominant offensively as the former Syracuse champ.

Odds: 2-1

Five possible Knicks targets

Pau Gasol

Versatile 7-footer has raved about Phil Jackson’s return to NBA as president and needs out of L.A. Averaged 17.4 points and 9.7 rebounds last season. Jax and Jose Calderon will plead for him to take a sharp discount with chance to play with his brother Marc in 2015-16.

Kris Humphries

Likes New York a lot. A bruising big who could make nice complement to Samuel Dalembert.

Jordan Hill

Former Knicks first-round pick traded for 2010 cap space has developed into an active rebounder and at least fits the price range as viewed as backup power forward.

Spencer Hawes

With Marcin Gortat out of price range, perhaps very serviceable 7-foot-1 Cleveland pivot would want to out of Ohio for the big lights of Broadway.

Jason Smith

More realistic signing. With Pelicans, 7-foot forward showed he has mid-range jumper and can block shots.