At his introductory news conference Tuesday, Masai Ujiri, the team's new vice president of basketball operations, said he's been in contact with Anthony and will meet with him soon.
The Nuggets offered Anthony a three-year, $65 million extension through 2014, but if he rejects it, the team will have to consider trading the forward who has guided them to seven straight playoff berths.
"I think I'm going to convince him to be a Nugget," Ujiri said, smiling. "No, I don't know, I can't make a judgment on that. Like I said, it's a process and until he tells me that ... we want him back, the city wants him back, ownership wants him back."
There have been hints that Anthony might be thinking about moving on: his mansion in the Denver area is on the market and at his New York wedding to TV personality LaLa Vazquez this summer, there was that now famous toast by New Orleans point guard Chris Paul about reuniting with Melo in Gotham to form a super-team along with Amare Stoudemire to counter the Miami Heat's terrific trio.
Anthony has never come out and said he wanted to be traded, however.
At his basketball camp this summer, Anthony dismissed all the speculation of his impending departure from Denver: "I've been hearing that for five years. I'm a Denver Nugget. I'm here, I'm with the Nuggets. I don't become a free agent until next year, if I decide not to take that extension."
He said then that he was just taking his time making a decision.
Team president Josh Kroenke, who is taking over the ownership duties from his father as a condition of Stan Kroenke's purchase of the NFL's St. Louis Rams, said Tuesday that he's had cordial conversations with Anthony and his agents, disputing reports of a recent contentious meeting.
"I haven't had a negative conversation with Carmelo Anthony since I've known him," Josh Kroenke said. "... I think he knows that he can come to me as an individual and we have that amount of respect to where we can talk about things openly in a non-combative way. So, anything that has been stated from sources behind sources, all of our talks have been cordial."
What about talks with his representatives, including agent Leon Rose?
"They've been perfect gentlemen, as well," Josh Kroenke said. "They've been great."
Coach George Karl said he hasn't talked to Anthony about his intentions.
"I didn't feel healthy enough to go to the wedding, so I have not seen him since then," Karl said. "We've had some communication through [assistant coach Tim Grgurich] and through Masai and some people, but I can't deny it kind of shook me a little bit. I really don't know" what he will do.
In addition to the Melo Matter, Ujiri faces questions surrounding J.R. Smith, who is under police investigation for allegedly choking a player during a pickup game at the team's practice facility recently.
Then there's uncertainty surrounding Karl, who's planning on returning to the sideline in September after missing the end of last season while fighting neck and throat cancer.
And if Anthony leaves, the Nuggets could be looking at lots of empty seats.
"I think there are a lot of challenges in this job, but what job doesn't have challenges?" Ujiri said. "How can I turn down a GM job in the NBA just because there are challenges with the job? I think it's a great job."
Ujiri pointed out that the Nuggets reached the Western Conference finals just two years ago and said the future looks bright under Josh Kroenke's leadership.
"There's a new passion, a new movement here," he said.
The Nigerian-born Ujiri's infectious enthusiasm and energy are good for the Nuggets, Karl said.
"I think Masai has a personality that fits the problems that we have," Karl said. "He's such a positive dude."
Like his predecessor Mark Warkentien, Ujiri will have to share power. He'll work with Josh Kroenke, Karl and longtime team adviser Bret Bearup.
"It's a team effort out here," Josh Kroenke said. "We're coming off three 50-win seasons, and I think that speaks for itself."
Karl, who looked rested and spoke with a stronger voice than he's had since he began chemotherapy and radiation treatment last spring, said he was going on a week's vacation before returning to prepare for training camp.
He said his recovery is expected to last well into the upcoming season and acknowledged that he'll have to continue to cut back for his health's sake.
"I'm not going to be a 10-hour-a-day guy anymore," Karl said. "I've been a delegator and a director for two or three years. It's going to continue to be more of that."
Karl isn't overly concerned about so many Nuggets, including himself, entering the final year of their contracts.
"It doesn't bother me. If I was coaching a bad team, I'd be a little more nervous," Karl said. "I think I'm coaching a good team that's going to win 45 to 55 games. That will probably get me another job if I don't have one here."
So, what advice would he have for Anthony?
"I would just tell him, I don't know if you're going to find a better city to live in than Denver," Karl said.