According to Rivers himself, yes it could.
"Part of it [the speculation] is true," Rivers told the Boston Herald. "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," Rivers said of his children. "That's important to me. We're all family men. We all have kids. Every year you've got to weigh what's best for your kids. That's just the way it is."
Sources told the Herald that Rivers was leaning toward leaving the Celtics after this season, but Rivers said he has not given any such indication to anyone.
"I don't get into it now," he told the newspaper. "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' children are all athletes, and the travels of both him and his wife to watch them play around the country have been well-documented. Jeremiah, who formerly played for Georgetown, will be a senior next season for Indiana University; Callie will be in her senior season for volleyball at the University of Florida; and Austin, who's become a bit of a YouTube sensation in his high school career, will be playing in his senior year of high school.
While Rivers was noncommittal either way, he said that whatever decision he makes, it will be absolute.
"The one I will say is I'm committed to Boston," Rivers said. "It's either [I] stay with the Celtics or I decide I need to stay more with the family."