BOSTON – After deciding to bring back Boston’s aging Big Three for another run at the NBA title, Danny Ainge knew he needed to surround it with more talent.

The Celtics’ general manager settled on former Dallas Mavericks shooting guard Jason Terry as one of the key pieces. Terry reportedly has agreed to a three-year deal for $15 million that is only waiting for the NBA’s moratorium on free-agent signings to be lifted July 11 for the deal to be finalized.

Brandon Bass reportedly has agreed to a three-year deal that is also being held up until the signing date. That gives Boston back its third-leading scorer, a 6-foot-8 forward who averaged 12.5 points in his first season with the Celtics.

Terry, who is one of the league’s top 3-point shooters, wouldn’t keep the Celtics from bringing back Ray Allen, who met Thursday with the Miami Heat. Salary-cap rules allow Boston to offer Allen more money than Miami.

“We really want Ray to come back,” Ainge said this week. “Time will tell.”

That would keep the Big Three intact to try for a second NBA championship — the 18th for the league’s most-decorated franchise. Paul Pierce is under contract for two more years and Rajon Rondo for three.

Ainge nearly dealt Allen, the top 3-point shooter in NBA history, at the trading deadline in a deal that would have signaled the end of the partnership that led the Celtics to the 2008 championship. The same group returned to the NBA finals in 2010, losing to the Los Angeles Lakers in seven games.

After the Celtics lost to Miami in seven games in this year’s Eastern Conference finals, Ainge waited for Garnett to decide if he wanted to retire and considered rebuilding with a younger roster. But Garnett agreed to terms on a three-year, $34.5 million deal.

Terry, who is 34, doesn’t make the Celtics much younger, especially if Allen returns. But he provides depth needed when Allen was hobbled with bone spurs in his ankle.

The 2009 NBA Sixth Man of the Year and a member of the Mavericks team that won it all in 2011, Terry came off the bench to average 15 points per game for Dallas last season. In his career, he has averaged 16.1 points and 4.7 rebounds.

Over five years with Atlanta and eight with Dallas, Terry is a career 38 percent 3-point shooter who has made 1,788 over his career, fourth-most in NBA history. Allen is first with 2,718.

During the 2011 postseason, Terry was the Mavericks’ No. 2 scorer, averaging 17.5 points per game, hitting three 3-pointers and scoring 27 points in Dallas’ Game 6 win to clinch a first title.

ALLEN SEEMS to be taking a serious look at joining Miami, planning to remain in south Florida until today.

Miami’s desire to add Allen is no secret. 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, saying Thursday would be “a big day” for the Heat.

Allen has been offered a $12 million, two-year deal by Boston. The Heat 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 otherwise.

Allen is coming off surgery to remove bone spurs from his right ankle but clearly can still shoot, and made a career-best 45 percent of his attempts from 3-point range this past season.

Also Thursday, NBA.com reported that the Heat would meet Saturday with another free-agent target, forward Rashard Lewis.