Melo spent two hours with the Lakers earlier on Thursday, will consider his options.
The New York Knicks reportedly met with Carmelo Anthony in Los Angeles on Thursday and will offer him a max contract in order to re-sign, as reported by the New York Daily News.
The 30-year-old had held a meeting with the Los Angeles Lakers earlier in the day, and that followed on from talks with the Chicago Bulls, the Dallas Mavericks and the Houston Rockets this week.
As one of the most in-demand free agents on the market, Melo has dominated the headlines for the past fortnight and he will continue to do so until he has reached a decision on his future.
However, it is understood that on Wednesday, the Bulls showed the first signs of pessimism in their pursuit of the Knicks star, as reports emerged that they had stepped up their interest in Pau Gasol.
It was suggested that the organisation got the impression that Anthony was likely to stay in New York, which would ultimately spell disappointment for the three Western Conference teams looking to sign him too.
The Knicks are undoubtedly in a strong position as they are able to offer their biggest name a maximum contract worth $129m over five years, whereas the other teams are restricted to offering up to $96m over four years.
In the case of Chicago, they are at an even bigger disadvantage due to salary-cap space, and they would only be able to offer Anthony around $16m per year.
It is expected that Anthony will take the weekend to look over his options and is likely to give his answer to the Knicks early next week over where he sees his future.
Despite a disappointing season last year for the Knicks in which they failed to make the playoffs, Anthony continued to impress with his scoring as he ended the regular season averaging 27.4 points per game.
Given the scoring struggles that the Bulls have suffered in the last two years, particularly with point guard Derrick Rose sidelined with two serious knee injuries, it appeared as though Chicago would be the perfect fit as they would provide Anthony with an immediate opportunity of winning an NBA championship.
Anthony has insisted that he is not so concerned with the financial aspects of his next deal, as he wants to play for a team that is able to compete at the highest level with his window of opportunity to win a title closing.
That in turn led to suggestions that he would not stay with the Knicks as they begin a rebuilding process under team president Phil Jackson, but the lure of playing at Madison Square Garden and the way in which his family has settled in the city have left Anthony in a difficult position.
New York remain the favourites to secure his signature for next season, but the Bulls, Mavericks, Rockets and Lakers all appear to be pleased with the way their pitches went, and now it remains to be seen where Anthony decides to land ahead of next season.