The New York Knicks are increasingly optimistic about their chances of re-signing star Carmelo Anthony even as he readies himself to talk to other teams next week, according to sources close to the situation.

Sources told ESPN.com that Knicks officials, while not willing to trumpet it publicly with free agency fast approaching, are quietly confident about their odds of retaining Anthony thanks in part to the idea that new team president Phil Jackson and the high-scoring forward have "connected" to some degree.

Knicks president Phil Jackson is planning to make a determined attempt to try to recruit Pau Gasol, his former center with the Lakers, a source says. Victor Decolongon/Getty Images

Furthermore, one source close to the process told ESPN.com's Ramona Shelburne that Jackson is planning to make a determined attempt to try to recruit his former Los Angeles Lakers center Pau Gasol to replace the freshly traded Tyson Chandler alongside Anthony on the Knicks' front line, despite the fact New York is limited to offering Gasol less than $4 million for next season.

Time will tell if the Knicks' internal confidence in retaining Anthony proves justified, given that he opted out of the final year of his contract at $23.3 million -- with Jackson urging him to opt in -- and will soon be courted face-to-face by a handful of top teams in big cities.

The 30-year-old officially becomes an unrestricted free agent on Tuesday at 12:01 a.m. and, as ESPN.com reported earlier this week, is planning to go on visits or hold meetings with the Chicago Bulls, Houston Rockets, Dallas Mavericks and Lakers all before the Fourth of July. It also must be noted as July 1 draws near that the Bulls and Rockets have likewise been radiating no shortage of positivity about their chances of stealing Anthony away from the Knicks.

The Miami Heat are likewise expected to have Anthony's ear if they choose to formally jump into the race, thanks to the close relationship between LeBron James and the Knicks' star, sources say. But Heat president Pat Riley -- after confirming a recent ESPN.com report that Miami has Anthony on its radar despite the challenges it faces just to get James, Dwyane Wade and Chris Bosh all re-signed -- has acknowledged that growing the Heat's Big Three into a Big Four is a "pipe dream."

Sources told ESPN.com this week that the Knicks swung their trade with the Mavericks to send out Chandler and the out-of-favor Raymond Felton to bring back a clutch of veterans in return -- headlined by point guard Jose Calderón -- in their belief that Anthony would relish the prospect of playing with the Spaniard. Calderon has been a perimeter threat and a beloved teammate everywhere he's played.