"Carmelo loves being a Knick, he loves the city, and he loves the fans," Rose said. "At this stage of his career, he just wants to explore his options."
Anthony can sign a maximum contract worth $129 million over five years with the Knicks. He can sign a maximum deal worth $96 million over four years with another team.
He has discussed the possibility of accepting less than a max contract to help the team that he signs with attract additional free agents. Anthony would consider signing with the Chicago Bulls, Houston Rockets or Dallas Mavericks, sources say.
The Miami Heat have also explored their available options in trying to pursue Anthony, ESPN.com reported earlier this month.
Anthony earlier this month noted that the idea of uprooting his family to another city would be a factor in his decision in free agency.
"The average person just sees opportunity to say that, 'Oh, Melo should go here, Melo should go there. I think he should do this, I think he should do that.' But they don't take into consideration the family aspect of it. Your livelihood. Where you're going to be living at. Do you want your kids to grow up in that place? In that city? Do I want to spend the rest of my career in that situation in that city? So all of that stuff comes into play," Anthony said in an interview with Vice Sports that was taped on June 3.
"My son goes to school (in New York). He loves it here. To take him out and take him somewhere else, he has to learn that system all over again, he has to get new friends. And I know how hard it was for me when I moved from New York to Baltimore at a young age. Having to work your way to try to make friends. And go extra to try to make friends and try to fit in and try to figure out the culture in that area.
"As far as this goes, basketball goes, it's hard to just say, 'OK, I'm going to go here, I'm going to make this decision, I'm going to do that. Because everybody's affected by that."
Anthony, 30, also said in the interview that he'd consider the "big picture" when making a decision on where to play next season.
"The average person is looking at it as next year, like it's just one year. 'Next year you win the championship if you go here.' We're looking at the big picture here now," Anthony said. "You're looking at the next six to eight years of your career, of the end of your career at that. So do you want to spend that much time in that place?"
Knicks president Phil Jackson said recently that he hoped Anthony would consider opting into the final year of his contract and testing free agency in the summer of 2015, but Anthony stated publicly throughout the season that he intended to become a free agent this summer.
Teams can meet with Anthony on July 1, the start of the NBA's free-agency period.
Anthony has already done some research on the city of Chicago, and the Bulls have reportedly done some homework on Anthony as well. According to league sources, Anthony has talked to at least one high-profile person who lives in Chicago about what it's like to be famous in the Windy City.
Bulls coach Tom Thibodeau has reached out to some of Anthony's former coaches to inquire about the seven-time All-Star, according to a report in the Chicago Sun Times.
ESPN.com reported in March that Anthony and Bulls center Joakim Noah talked about playing under Thibodeau during the All-Star break and that the conversation turned into a recruiting pitch from Noah to Anthony.
Jackson said late last month that he's "not losing sleep" over Anthony's free agency but is "definitely concerned" about the idea of Anthony signing elsewhere. Anthony has said publicly that he would like to stay in New York but also wants to be in position to win an NBA championship.
The Knicks don't appear to be on the verge of title contention. New York won just 37 games last season and is projected to be over the salary cap this summer, which will limit its ability to sign free agents.
Jackson and the Knicks are expected to try to sell Anthony on the idea that they can add a star to the roster in the summer of 2015, when they are expected to have significant cap space.