WALTHAM, Mass.

The Boston Celtics aren’t going to get what they really need with the No. 16 pick in Thursday’s NBA draft.

They won’t be able to select a coach, unless general manager Danny Ainge has found a loophole in league rules that allowed him this week to trade Doc Rivers to the Los Angeles Clippers. And, with their only pick of the night coming in the middle of the first round, they won’t find the player that they need, either: A younger version of Kevin Garnett or Paul Pierce to replace the aging veterans who are increasingly showing signs of slowing down.

“I think it’s a fairly deep draft. I just don’t think it’s a star-laden draft,” Ainge said this week after explaining why he agreed to let Rivers go. “I definitely think there are some good role players in the draft.”

Five years after assembling the New Big Three, the Celtics seem finally ready to tear down the roster that won the franchise’s unprecedented 17th NBA title in 2008 and returned to the finals two years later. Ainge all-but confirmed that it’s time to rebuild this week when he let Rivers go to the Clippers in exchange for a first-round pick in 2015, a move that could be followed by the departures of Pierce and Garnett.

Garnett is 37 with a no-trade clause and a contract that will pay him $23.5 million over the next two years; he has openly discussed retiring. Pierce, the longest-tenured member of the team, is due to earn $15.3 million next season, when he will be 36; he could be bought out for $5 million, with the deadline at the end of the month.

Without Garnett or Pierce, the Celtics would have few blocks to build on.

Point guard Rajon Rondo is a top ball-handler with a questionable shot who is coming off surgery for a torn ligament in his right knee. Guard Avery Bradley is a defensive specialist who missed the first half of last season with injuries to both shoulders.

Jeff Green, who returned after missing a year because of heart surgery, could take up the minutes that Pierce had provided. But with the health of Fab Melo and Jared Sullinger in question, the roster is largely lacking big men beyond Garnett.