In fact, according to the Boston Herald , he might be leaning heavily toward quitting.
For his part, Rivers says he hasn't decided anything and won't until he huddles with his family this summer to discuss their options, an annual event.
Rivers addressed the speculation on Tuesday, saying, "Part of it is true. Every year I sit down in the middle of the summer and I have a family discussion. We talk about what we want to do. That's nothing new, but every year it gets stronger and stronger. And I think people are making some common sense reads. I've got three seniors next year, two in college and one in high school. That's important to me.
"Every year you've got to weigh what's best for your kids. That's just the way it is. But, I don't get into it now. I don't talk about it. I've never told anyone one way or the other, and that's how it's always been."
Rivers has a son who is a senior basketball player at Indiana and a daughter who is a star senior on the volleyball team at Florida.
His son Austin, meanwhile, is a top hoops prospect wrapping up his high school career.
Rivers says he avoided discussing a contract extension with team president Danny Ainge earlier in the season. He currently has just one year left on his deal.
He also says the struggles the Celtics have had this season have nothing to do with his decision.
"The one (thing) I will say is I'm committed to Boston. It's either stay with the Celtics or I decide I need to stay more with the family," Rivers told the Boston Herald .
He went on, "Well, I don't really think anybody knows what next year's going to be. Kevin (Garnett)'s going to be healthier next year, because it's going to be a year further away from the surgery. Hopefully Ray (Allen) will be back, and Paul (Pierce) will still be a force. You never know what can happen with trades and free agency.
"So I think the demise of the Celtics may be greatly exaggerated. People think this is it, and I don't think anyone in our office feels that way. But as far as I'm concerned, I can tell you I try never to make a decision in the season. That's the worst time. You're emotional either way about it."