"I'm still keeping it [mellow], still keeping it cool, man. It definitely kind of tests you, can put you to the test," Anthony said after the Knicks' 111-104 loss to the Cleveland Cavaliers. "You have to dig deep within yourself to get through it on a day-to-day basis, figure out a way how to still go out there and play at a high level every night, play hard, lead this team.
"That's kind of where you have to dig deep at, despite of everything that's going on, that's surrounding -- I don't even want to say us -- me. It's testing me. It's testing my will. It's testing me as a human being. It also is making me stronger throughout this process."
Anthony has been the subject of trade rumors recently, with Knicks president Phil Jackson and the front office looking for potential deals to move the 13-year veteran.
The Cavs rebuffed the Knicks' attempt late last month to trade Anthony for Kevin Love, sources told ESPN's Marc Stein and Ramona Shelburne.
Stein and Shelburne reported earlier this week that the Knicks continue to pursue Love in advance of the Feb. 23 trade deadline despite the Cavaliers' unwillingness to part with him. Love said on Friday that he believes he'll remain with the Cavs "for a long time."
Sources told Stein and Shelburne the Cavaliers maintain an interest in Anthony -- which would pair him with James -- but only if a deal can be struck without the Cavs surrendering Love.
The Knicks, who have lost 17 of their past 23 games, also have spoken to the LA Clippers and Boston Celtics about potential deals involving Anthony.
Anthony has a no-trade clause and would need to waive it before any deal can be consummated.
He said earlier this week that he hasn't thought about waiving his no-trade clause because Knicks management hasn't discussed any potential deals with him.
Anthony said on Saturday that being around his family and teammates helps him maintain a positive outlook amid all of the trade rumors and losing.
"My son, family, friends. Those are things, people that keep me positive, keep me happy," he said. "And then when I get to the gym it's just all about basketball and being around kind of my teammates and seeing the vibe is still there between us, between everybody. Everybody is still positive about what we have going on and what we're trying to do. So that's the way I'm dealing with it."
Anthony averaged 30 points in a recent seven-game stretch from Jan. 19 to Jan. 31 but has struggled in the past two games, missing 30 of 42 shots.
He was booed sporadically by the crowd at Madison Square Garden on Saturday.
"I mean, you are what the back page [of local newspapers] says you are. Fans read that. And they react to that," Anthony said. "I got to get in the gym. I've got to get in the gym tomorrow and work on my shot and they won't boo me."