Melo has been the subject of constant trade rumors, and he called the situation "an emotional roller coaster," according to Marc Berman of the New York Post.
Anthony is in a state of flux, as his no-trade clause allows him to block a move to any team.
Berman reported Monday that Melo has made it clear to the Knicks he only wants to be traded to the Houston Rockets in order to play alongside James Harden and Chris Paul.
That puts New York in a bind, as it must either grant his wish and potentially accept less than market value in return, or leave him on the roster and slow the rebuilding process.
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Although the 33-year-old veteran had a strong statistical season in 2016-17, averaging 22.4 points, 5.9 rebounds and 2.9 assists per game en route to his 10th career All-Star nod, the Knicks struggled as a whole.
They finished a disappointing 31-51 in the midst of a public feud between Melo and team president Phil Jackson, who has since parted ways with the organization.
The Knicks have some promising pieces in place in the form of Kristaps Porzingis, Willy Hernangomez and Frank Ntilikina, but their playoff chances in 2017-18 appear bleak regardless of whether they keep Anthony in the fold.