Less than a week before the belated start of training camp, their roster consists of just six signed players.

The Celtics will find themselves doing a lot of 3-on-3 drills if that doesn’t change by the end of next week.

President of basketball operations Danny Ainge, though, is confident he will have the roster stocked near or at the 15-player maximum by the time Coach Doc Rivers conducts his first practice this upcoming Friday morning.

“Hopefully, we’ll be close on Dec. 9, but there may be some straggling players coming in,’’ said Ainge. “Hopefully when we start training camp, we’ll at least have 10.’’

Ainge and Rivers, seated next to him at a press conference on Thursday morning, laughed at that last remark, knowing how tough it would be if they didn’t have enough players to field two five-man units.

The Celtics have nine openings to fill, and three of them could be taken care of by signing restricted free agent Jeff Green and draft picks JaJuan Johnson and E’Twaun Moore, who have had the start of their careers on hold since July 1 because of the NBA lockout.

The team has already had discussions with Glen Davis and Delonte West, who could leave the Celtics as free agents.

With little money to spend on other free agents – the Celtics will be using the $3 million mid-level exception and the veteran’s minimum – Ainge won’t be chasing the prime players available.

As the roster is put together on the fly, Rivers will have 16 days to get his team ready for the Christmas Day opener in New York against the Knicks, which will start at noon and be the NBA’s kickoff game. That will make for an interesting training camp, especially with the long layoff since the end of the 2010-11 season.

Rivers will be relying heavily on veterans Kevin Garnett, Paul Pierce, Ray Allen, Rajon Rondo and Jermaine O’Neal to set the tone for whatever his team looks like.

“I think we have a really professional group,’’ said Rivers. “They’ll be in a gym. That’s who they are. Every time I go to dinner somewhere in Boston I hear a story about one of them at some YMCA or something, and that’s a good thing. They’re going to work on their craft.’’

The Celtics will have the same starting lineup that was used in the playoffs last spring, but there will be chemistry issues as a new bench is formed – unless Green, Davis and West are all back together as the main reserves.

“I think we’ll be fine,’’ said Rivers of having cohesiveness. “That is going to be a challenge with the additions. We don’t know who we’re going to add yet. We have a list and we’re going after that list.

“When you’re integrating half a team to another half a team, it’s going to be (tough). But we’re not the only team that’s doing that. But like Danny said, we do have a core group that is familiar with what we do.

“Obviously, they’re going to be extremely important to start the season and help carry whatever new guys we have. I expect us for the first game to be ready. We may have to put in more work to get there. We may have to go doubles in training camp and through the preseason to get there, but I think we can get there.’’

The Celtics, who will hold camp at their training facility rather than Salve Regina University as has been the case in recent years, have preseason games scheduled for Dec. 18 in Toronto and Dec. 21 against the Raptors in Boston.

That leaves 14 days of practices before the Celtics spend Christmas Day in New York City to get the season going.

The Celtics are expected to receive the revamped schedule early next week with 66 games jammed into less than 18 weeks. Having nearly four games per week might cut down on the in-season practices Rivers will conduct.

“I’ve done some research,’’ he said, “and. I know the last time this happened with the 50 games (in 1999), there were some coaches who didn’t have any practices at all during that season. There were some who did it the other way. We’ll figure it out. I can guarantee that.

“At the end of the day, we’re going to have to figure out the rhythm that works for our team.’’