Jackson's optimism stems in part from the rapport he's established with Anthony through the Knicks' meetings with the free agent forward.
"I felt really good about my conversation with Melo," Jackson said. "We really struck a chord. The two of us, I think, feel really passionately about what we're trying to get accomplished. It's his ability to stay, be patient, lead and watch us develop a winner. There's no instantaneous winner that we think is going to happen to the Knicks right now, but we're going to be a lot better."
Jackson said the Knicks have made five different contract offers to Anthony, one of which is believed to be a maximum deal of $129 million over five years.
Anthony's agent, Leon Rose, told ESPN.com on Wednesday afternoon that his client "hasn't made a decision yet."
"No decision yet," another source said. "Still up in air."
Anthony visited the Chicago Bulls, Dallas Mavericks, Houston Rockets and Los Angeles Lakers last week in addition to meeting with Jackson and the Knicks in Los Angeles.
The Lakers are prepared to offer Anthony a four-year, $97 million contract, the most allowed under the collective bargaining agreement. For the Bulls to make an offer approaching a maximum contract, they'd have to orchestrate a sign-and-trade for Anthony.
Jackson said he has texted Anthony several times in recent days and hasn't heard back from the seven-time All Star.
"We have alternative plans -- Plans B, C, D, E and F -- but so far, we're still in Plan A, and that's the first kingpin we have to have in this whole situation," Jackson said of Anthony, who was second in the NBA in scoring last season (27.4 points per game) and pulled down 8.1 rebounds per game.
Jackson added that Anthony and his advisers are "amenable to what [the Knicks] are trying to accomplish."
The first-year president was asked if he expected a "positive outcome" for the Knicks if Anthony decides to sign elsewhere.
"Yes," he said. "It means we go forward with some of the other plans that we have, secondary plans, to try to sustain this team. Whether we turn to more veteran support or we go a different direction, [there will be] opportunities."
Jackson said he has also spoken with free-agent forward Pau Gasol about joining the Knicks.
"I think he would like to play with Carmelo, and I think he would like to play with a winner," Jackson said of Gasol, whom he coached in Los Angeles during two NBA title runs.
Gasol is also being courted by the Bulls, Thunder and Lakers, among others. He would need to take a significant pay cut to sign with the Knicks. Gasol made $19 million last season, but the Knicks have only the $3.3 million exception to offer free agents at the moment.
Jackson has talked recently with teams about the possibility of trading Amar'e Stoudemire to unload his $23.4 million salary, sources say. That move would free up cap space and increase the money the Knicks can offer free agents. Jackson hasn't yet found a team willing to absorb Stoudemire's salary.
With the Lakers in play for both Gasol and Anthony, Jackson was asked if it was awkward to compete against his fiancee, Lakers president Jeanie Buss, for free agents.
"No, no. We talked about this before," Jackson said. "We're going to be in a place where there are going to be players who both of us want and we just have to deal with it. We'll put our best pitch forward and we just accept that as part of the game. It is what it is. I think these owners, and the position that I'm in, you have to understand that it's just part of the game."
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