Heat President Pat Riley is currently at his Los Angeles-area home, but Tanner said Allen's meeting with the Heat would be in South Florida.
The NBA free-agency period opened Sunday, with free-agent signings not allowed until July 11, as the league computes the 2012-13 salary cap. Allen spoke with the Heat by phone Monday.
According to NBA.com and ESPN, Allen is scheduled to meet Friday with the Los Angeles Clippers, who are in position to not only exceed the Heat's $3.1 offer of the taxpayer mid-level exception, the most the Heat can offer, but potentially also offer a starting job alongside Chris Paul.
Allen has a reported standing offer on the table to return to the Boston Celtics at twice the yearly salary the Heat can offer, but apparently was not pleased with the way he was stripped of his starting job there last season in favor of Avery Bradley.
With the Heat, Allen also would be counted on as a reserve, with Dwyane Wade locked in at shooting guard.
The situation in Boston grew more intriguing Tuesday afternoon, with the Celtics moving close to an agreement with Dallas Mavericks free-agent guard Jason Terry, which would seemingly push Allen further down Boston's rotation, should he return there. The Celtics' salary-cap situation would allow them to sign both Terry and Allen.
As for the Clippers, they currently are in pursuit of free-agent guard Jamal Crawford, which would be for the role Allen could otherwise fill.
Asked to define Allen's free-agency priorities, Tanner declined.
The Heat already have begun somewhat of a recruiting effort for Allen, with LeBron James posting on his Twitter account last week, "While watching the Draft my son Bryce ask "Is Ray Allen gonna play for the Heat". I said "I don't know, I hope so".
Allen started for the Celtics in their seven-game ouster at the hands of the Heat in the Eastern Conference finals after Bradley was sidelined by a shoulder injury.
Allen also is being pursued by the Memphis Grizzlies and Minnesota Timberwolves, but those two teams, according to NBA.com, have yet to secure visits from the 36-year-old 3-point specialist.
Riley last week stressed 3-point shooting as an offseason priority, as a means to open the floor for Wade, James and forward Chris Bosh. The Heat also have reached out to New Orleans Hornets free-agent forward Rashard Lewis, another 3-point specialist.
Over the weekend Celtics coach Doc Rivers expressed confidence in Allen returning to Boston. However, he backed off somewhat during a Tuesday radio appearance on the "The Dan Patrick Show."
"I don't know," Rivers said. "We're working hard. He has a lot of options and that's the bad news for us. It'll be interesting. I wish I had a feel on it. Usually I do. But I can tell you in this one I don't."
Allen currently is recovering from surgery to remove bone spurs from his right ankle, an issue that led to his removal from the Celtics' starting lineup and his limited playing time at the end of the season.
"It was amazing that Ray was even able to play at all throughout the playoffs," Celtics President Danny Ainge told the Boston Globe. "We feel like he will fully recover shortly. I think he'll be playing basketball within the next few weeks."
Bird: Easy way out
In an interview with ESPN, former Indiana Pacers President Larry Bird appeared to be questioning the motives of stars such as Allen offering to play at a discount with teams such as the Heat in bids for championship rings.
"The one thing that bothers me the most is guys taking big pay cuts for a year to go down there and try to win a championship," he said. "There's a lot of guys that like to ride the coattails of the best, and they'll take a pay cut just to have an opportunity to win that ring."
He did not, however, take issue with James leaving the Cleveland Cavaliers to sign to play with the Heat in 2010.
"I always say you have to play by the rules, and if that's the rules, that's the rules," he said. "But to have the best player and probably the fifth- or sixth-best player and a top-20 player? That's tough to compete against."
Bird's Pacers lost to the Heat in the Eastern Conference semifinals, with Bird stepping down shortly thereafter.