Anthony is expected to attend the meeting, though his presence is not a certainty.
The meeting is being initiated by Anthony, who has grown tired of hearing his name mentioned in trade rumors. His desire is to stay in Denver and he wants assurances from the Nuggets that they will not trade him. Anthony's party expects to get those assurances on Monday, according to the sources.
If the Nuggets don't commit to building around Anthony -- and instead demonstrate a willingness to trade him -- he will ask to be moved. Believing he will remain with the Nuggets, Anthony has not put together a list of teams he wants to be traded to.
When reached by Denver media on Saturday, Anthony's agent denied trade talks.
"I am only coming to Denver to support Melo on his DUI court case Tuesday. Any planned discussions with the Nuggets will be about any penalty if he is charged," Calvin Andrews told The Denver Post.
A source told the Rocky Mountain News that Anthony won't be at the meeting.
Anthony was arrested on a DUI charge in Denver on April 14. The Nuggets forward was arrested on Interstate 25, police said. He was alone in the car and pulled over for weaving and not dimming his lights.
Detective Sharon Hahn said Anthony failed a series of sobriety tests. He was charged with DUI, then taken to police headquarters before being released to a "sober responsible party," Hahn said.
In a phone conversation later Saturday with Denver TV station KDVR, Andrews attempted to explain the genesis of the reports.
"Somebody could have told [the reporter] I was coming into town, and could have assumed I was trying to shake things up, but that is just not the case," reiterated Andrews.
Andrews was asked by the TV station whether the public should still assume trade talks won't surface during a conversation about Anthony's DUI case.
"I'm sure it will come up, but the bottom line is I don't have a meeting to talk about trades," Andrews said.
To Andrews' knowledge, Anthony has not demanded the Nuggets talk to him either, nor will Anthony be in Denver to talk with the organization himself at the beginning of the week.
"He won't even be in Denver on Monday. Melo will be in Chicago with a USA basketball conference on Monday," Andrews told KDVR.
Andrews was also asked whether Anthony would attempt to talk to the Nuggets via teleconference.
"There is no plan [for Anthony] to talk on Monday, Tuesday, Wednesday," Andrews said.
While a source told the Rocky the report is "accurate," additional messages were left for Andrews asking him to discuss its accuracy. They were not immediately returned to the Rocky.
Speculation about a deal involving Anthony began in May when reports surfaced that New Jersey had contacted Denver about a trade for the two-time All-Star forward. While the likelihood of a trade to the Nets was never high, executives around the league insisted that Nuggets coach George Karl was indeed ready to trade Anthony.
Denver denied that it was looking to trade Anthony, but the rumors have persisted. Detroit recently offered Chauncey Billups and Tayshaun Prince for Anthony, but the Nuggets weren't interested. Denver countered with an offer of Allen Iverson or a package built around Marcus Camby, but the Pistons are only interested in Anthony.
Executives with other teams say Denver's management group is divided over Anthony's place with the team. They say Karl wants to trade him, but that general manager Mark Warkentien and club advisor Bret Bearup are against the move.
Anthony, 24, averaged 25.7 points and a career-high 7.4 rebounds last season but was unable to get the Nuggets out of the first round of the playoffs for the fifth straight season. Anthony struggled badly in this year's playoffs, averaging 22.5 points on 36.4 percent shooting in a sweep by the Los Angeles Lakers.
Chris Broussard covers the NBA for ESPN The Magazine. Information from The Associated Press was used in this report.