After their big sit-down with Carmelo Anthony in Los Angeles on Thursday, the Knicks are feeling “positive” about their chances of re-signing him, according to a source with knowledge of the meeting.

Anthony received Knicks president Phil Jackson’s message “well” during the meeting, in which the Knicks verbally offered Anthony a maximum contract worth $129 million over five years.

A Yahoo! Sports report Friday stated that Anthony and Jackson are "largely aligned."

Anthony hadn’t made a decision as of early Saturday afternoon. He is taking the holiday weekend to mull over his offers, a source told ESPN The Magazine’s Chris Broussard.

Anthony has several offers to consider.

The Los Angeles Lakers have offered Anthony a maximum contract of $96 million over four seasons.

The Houston Rockets hope to put themselves in position to offer Anthony a max contract worth $96 million over four years.

The Chicago Bulls, another main suitor for Anthony, seem to be on the verge of signing European forward Nikola Mirotic, which would compromise their cap space and impact their offer to Anthony.

Such a move would not preclude the Bulls from acquiring Anthony as a free agent, but that route would almost certainly mean they would have to do it with a sign-and-trade using Carlos Boozer. That would require the Knicks' cooperation.

Broussard reported earlier this week that the Knicks would not be willing to participate in a sign-and-trade for Boozer.

The most Anthony could make if he was signed and traded would be $96 million over four years, per CBA sign-and-trade rules.

The Dallas Mavericks, another suitor, have about $17 million in cap space after signing Dirk Nowitzki to a three-year, $30 million deal. That cap space shrank further Saturday afternoon when they re-signed point guard Devin Harris.

So the Knicks' offer of $129 million over five years is the largest and longest of all of his suitors.

For what it's worth, Anthony has said he'd be willing to accept less than maximum money if it helped the team he signed with acquire free agents.

A league source confirmed that Anthony, if he re-signs with the Knicks, would still be open to taking less than maximum money, as the New York Post reported earlier Saturday.

Per CBA rules, a player's salary can decrease by as much as 7.5 percent per season. So if Anthony signs a max deal with the Knicks, he can accept a contract that pays him as little as $20.85 million. That’s a savings of $3.4 million compared with what Anthony would get in the second year of a max contract with maximum raises.

This kind of pay cut would give the Knicks $3.4 million more to spend on free agents in summer 2015, when they hope to attract a big-name player to suit up alongside Anthony.

But there are indications that Jackson is hoping to rebuild the roster for the 2014-15 season. One major development along these lines occurred shortly before the draft when Jackson flipped Tyson Chandler and Raymond Felton for Mavs guards Jose Calderon and Shane Larkin, big man Samuel Dalembert and two second-round picks.

The Knicks also talked to teams about dealing Iman Shumpert prior to the NBA draft and have talked to at least one team about trading Amar'e Stoudemire, according to a source. Stoudemire is entering the final year of his contract this season and is scheduled to make $23.4 million. The trade and discussions of moving Shumpert and Stoudemire suggest Jackson is taking an aggressive approach to overhauling the Knicks' roster.

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