A source close to the situation told the Sun Sentinel late Sunday night, "there is an in-person meeting being scheduled for next two, three days."
Confirmation of the meeting came amid a wild flurry of media reports that ranged from the Cleveland Cavaliers surpassing the Heat as the free-agency front-runner for James, to the Cavaliers working to create salary-cap space to accommodate James, to fellow Heat free-agent teammate Chris Bosh being poised to a move to the Houston Rockets amid the James uncertainty, to ESPN speculation of Carmelo Anthony replacing Bosh alongside James with the Heat.
The most-recent wave of conjecture began hours after agent Henry Thomas, who represents Bosh and Heat free-agent guard Dwyane Wade, told the Sun Sentinel that previous speculation about his clients had been wildly off-base.
While James has maintained a low-key presence since Tuesday's start of free agency, Riley has been scouring the free-agent market for players to bolster James' supporting cast, including recent meetings with Pau Gasol, Trevor Ariza, Luol Deng and Marvin Williams.
While the free-agency negotiating period opened July 1, free-agent contracts cannot be signed until Thursday, at the end of the NBA's annual summer personnel moratorium.
James' agent, Cleveland-based Rich Paul, has taken meetings in recent days with potential James suitors, including the Los Angeles Lakers, Phoenix Suns, Houston Rockets, Dallas Mavericks and Cleveland Cavaliers.
Adding to the intrigue was the private plane of Cavaliers owner Dan Gilbert arriving Sunday at Fort Lauderdale Executive Airport, then leaving hours later. While Gilbert posted on Twitter he was not aboard, it is possible a member of the Cavaliers' front office beat Riley to the first face-to-face meeting between a team executive and James.
James had been with the same agency as Wade and Bosh when he signed along with those two to join the Heat in July 2010. He later moved to the agency started up by Paul, a long-time Cleveland-based friend.
James, Wade and Bosh last month all opted out of the final two years of those contracts signed with the Heat in 2010, each leaving in excess of $40 million on the table in exchange for the right to again become free agents.
The Heat have advanced to the NBA Finals in each of James' four seasons, winning consecutive championships, the first of James' career, before falling 4-1 to the San Antonio Spurs last month in the 2014 NBA Finals.
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