A person familiar with the situation told The Associated Press that the free agent guard visited the Heat in Miami on Thursday. Allen was planning to remain in South Florida until Friday, according to the person who spoke on condition of anonymity because no details of the meeting were publicly revealed.
The news comes as the Clippers have agreed to terms with Jamal Crawford and Chauncey Billups, while passing on Allen, according to the L.A. Times.
"With the Clips canceling their meeting with Allen, it seems all but assured Ray Allen will be playing for the Heat next season," CBSSports.com's Royce Young says.
Miami's desire to add Allen is no secret. League MVP LeBron James has tweeted about the notion, and posted a doctored-up image of Allen wearing a Heat jersey on his Facebook page earlier this week with the message, "This looks damn good to me."
And Dwyane Wade posted a cryptic message on his Twitter account Wednesday night, saying Thursday would be "a big day" for the Heat.
No deal could be finalized until at least July 11 because of the NBA's moratorium.
Allen has spent the last five seasons with the Boston Celtics, who have offered the NBA's 3-point field goal leader a $12 million, two-year deal. The Heat who have ousted Boston from the past two NBA postseasons can only offer Allen the mini mid-level exception, which would pay about $3 million this coming year.
Allen averaged 14.2 points for Boston this past season.
From an offensive standpoint, Allen would seem to be a perfect fit because the Heat have spent two years trying to surround James, Wade and Chris Bosh with shooters who extend defenses and create room around the basket. Miami was 9-1 in the playoffs when connecting on at least eight 3-pointers in a game, and just 7-6 when not.
Allen is coming off surgery to remove bone spurs from his right ankle. But he clearly can still shoot, and made a career-best 45 percent of his attempts from 3-point range for the Celtics this past season.
Also Thursday, NBA.com reported that the Heat would meet with another free-agent target, Rashard Lewis on Saturday.