BOSTON — The Miami Heat will get to make their sales pitch to Celtics free agent Ray Allen.

A person familiar with Allen’s plans said the free-agent shooting guard will visit with Heat officials Thursday.

The Celts say they still have interest in keeping Allen but secured insurance at the position.

According to two league sources, the team reached agreement on a three-year contract for former Dallas guard Jason Terry.

Terry, 34, was the NBA’s Sixth Man of the Year in the 2008-09 season. A year ago he averaged 15.1 points per game, shooting 43 percent in 63 games.

Terry has been known as a wiry defender and capable transition player. His spot-up style would work nicely with Rajon Rondo’s drive-and-dish game.

In his 13-year career, Terry is averaging 16.1 points and 4.7 assists. He is a career 44.8 percent shooter who hits 85 percent from the line.

One source stressed that the Celtics remain interested in Allen, who has talked with officials from Memphis and Minnesota this week, and plans to meet with Miami on Thursday and the Los Angeles Clippers on Friday.

A combination of Terry and Allen would give the Celtics a strong mixture of 3-point shooting, though neither likely would start ahead of Avery Bradley.

There also would be the question of playing time. Allen, who looms as a likely starter for the Clippers, appears to want a more prominent role than the way Coach Doc Rivers’ rotation may be unfolding.

Terry’s emergence as a Celtic also calls into question the team’s commitment to Mickael Pietrus, who is still waiting for a call from the team.

According to Pietrus’ agent, Bill McCandless, Pietrus has been contacted by four other teams, one with stronger interest than the others. Pietrus has talked directly with officials from two of those teams, including one coach.

Allen is one of Miami’s top offseason targets, so much so that even LeBron James tweeted last week that he hopes to play alongside him next season. Allen would have to take less money than he almost certainly could make elsewhere.

Miami can offer Allen only the mini mid-level exception worth just more than $3 million for next season, or roughly half what the Celtics are willing to pay to keep him. Still, Allen’s willingness to even listen suggests that Miami’s financial limits may not be a deterrent to a deal.

The Heat made just under 36 percent of their 3-point attempts last season. Mike Miller (.453) and James Jones (.404) led the Heat in accuracy from beyond the arc, though Miller is sorting out what he will do next season with back and foot issues.

Allen would figure to be a perfect fit with Miami because the Heat want to surround James, Dwyane Wade and Chris Bosh with shooters who extend defenses and create room around the basket.

That approach worked for Miami in the playoffs – the Heat were 9-1 when making at least eight 3-pointers in playoff games (7-6 otherwise), and hit 14 in the finals-clincher over Oklahoma City.

Allen has made at least 100 3-pointers in 15 of his 16 seasons, the exception being when he connected on 74 in the shortened 50-game schedule of 1998-99.

He’s established career bests for accuracy in each of the past two seasons, first making 44 percent in 2010-11, then 45 percent this past year. His 2,718 career 3-pointers are the most in NBA history.

This round of free agency has a much quieter feel for Miami than the summer of 2010. For example, the Heat owner, Micky Arison, tweeted Sunday that he was beginning a trip to Europe — a far different trek from what he, Riley, Coach Erik Spoelstra and others embarked on two years ago when they began wooing James and Bosh to join Wade in Miami.

The selling point that summer was “sacrifice,” and that hasn’t changed.

James, Bosh and Wade all took less money than they could have made elsewhere to allow deals to fall into place for Miami in 2010.

Last summer, Shane Battier accepted a deal worth $3 million annually.

That’s about all Miami can offer anyone this summer as well. Barring any trades, the biggest chip Riley has to dangle is the mini mid-level.