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.