BOSTON – Soon after the Boston Celtics’ season ended, on the last day possible, Coach Doc Rivers finally got a chance to sit down with General Manager Danny Ainge and discuss the draft that was just a week away.

“The first name and the first tape he showed me” was Avery Bradley, Rivers said after the Celtics took the Texas guard with the 19th selection in the NBA draft. “It was a guy he really wanted to show me. And then he said, ‘I don’t think he’s going to be there.’ “

Bradley was there when the Celtics got around to making their pick Thursday night, exactly one week after they lost to the Los Angeles Lakers in Game 7 of the NBA finals.

“It was a great feeling to know I could be a part of an organization like this and get a chance to learn from the guys on the team,” Bradley said.

“I feel like the coaching staff there is going to help me get better and better. I can also learn from older guys like (Rajon) Rondo, who can help me become a better point guard.”

With their second-round pick, No. 52 overall, the Celtics picked Notre Dame forward Luke Harangody, who averaged 21.8 points and 9.1 rebounds as a senior last season.

Now the question is: Who will coach them?

Rivers has said he might step down to spend more time with his family; he has three sons and a daughter, all athletes, and he hasn’t had much time to see them play.

“I don’t know yet,” Rivers said in a TD Garden hallway shortly after the first round of the draft. “I’ll have a decision very soon.”

Rivers said he was looking at July 1, which is also the start of free agency for players, as the deadline. In the meantime, Ainge and the Celtics’ owners have been lobbying him to stick around.

“They’ve been doing their jobs, I’ll put it that way,” Rivers said. “So have the players. They’ve been very vocal in their support. But that’s good. We’re very close.

“(Ainge) is my boss and he’s also one of my best friends. You look around the league and you don’t see that.”

Rivers said the hope is that Bradley, a shooting guard in his only year at Texas, will serve as Rajon Rondo’s understudy. The Celtics have lacked a dependable backup point guard even as they reached the finals twice in three years, winning their 17th NBA title in 2008.

“He’s really a solid backup,” Rivers said. “He could be a starter one day in the league. It’s tough to do that when Rondo’s in front of you, but he has a huge upside.”

The 6-foot-3, 180-pound Bradley averaged 11.6 points last year. As a high school senior, ESPN named him the national player of the year and the No. 1 prospect in the country.

Bradley is known as a strong defender and good outside shooter, but a weak free-throw shooter. Rivers’ sons played against him in summer leagues and raved about his defense.

“He’s an NBA defender right now,” Rivers said. “He can play point guard defense against anybody in the league.”

Not expected to return: Celtics big man Rasheed Wallace, who told Rivers during the finals he would retire after the season.

“He was pretty definite. He basically said he was finished,” Rivers said.

“Nothing’s happened, so he obviously has an opportunity to change his mind.”

That puts a priority on finding another big man, either elsewhere in the draft or in free agency. Starting center Kendrick Perkins tore ligaments in his right knee and isn’t expected to be ready to start the season.