The teams have no plans to speak again, the sources said, and the Clippers are preparing to move on and hire a coach this week.
Celtics president of basketball operations Danny Ainge, meanwhile, confirmed to The Boston Globe that the talks between the teams had ended.
Ainge told the newspaper the Celtics have told Rivers they want him to return to coach the team next season.
"He has been told that all along," Ainge told the Globe.
Ainge and Rivers were to talk Wednesday in a previously scheduled meeting, Ainge told the Boston Herald.
"He's coming to town," Ainge said. "He was coming to town before the events of today, so we were planning on meeting tomorrow anyway."
The question hanging over the Celtics now is whether Rivers still desires to return after this publicized flirtation with the Clippers and his obvious uneasiness about a rebuilding process in Boston.
If he does not want to continue on as the Celtics coach, he could simply retire or return to the broadcast booth. It is not known how that would affect Garnett, who would only have waived his no-trade clause to follow Rivers to the Clippers, or Paul Pierce, who has said he wants to remain a Celtic, but can be bought out of the final $15.3 million on his contract for $5 million by June 30.
That uncertainty has league observers skeptical the talks have died for good.
Said one league source: "It's dead until it comes back to life again."
A Clippers source told ESPN The Magazine's Chris Broussard that right now talks are stalled, "but never say anything is completely dead in the NBA."
After what sources described as "substantive" discussions on Monday, the talks broke down Tuesday morning when the Clippers "refused to budge" on Boston's latest proposal that asked for DeAndre Jordan straight up for Garnett, and two first-round draft picks as compensation for allowing Rivers out of the final three years and $21 million of his contract.
On Monday the teams had been discussing deals that helped create financial flexibility for the Celtics. After relenting on an earlier demand that young point guard Eric Bledsoe be included in the deal, Boston wanted to include Courtney Lee (who has three years and $14.4 million remaining on his contract) and Jason Terry (two years, $11 million).
ESPN.com reported earlier Monday that the Clippers were willing to take on the contract of Lee or Terry -- but not both.
Boston then countered with a simplified offer of two first-round picks as compensation for Rivers, and Jordan for Garnett. The Clippers decided that was still too steep of a price to pay, and chose to hold on to both their young players and draft picks to use in future moves to upgrade their roster.
A Clippers source insists the team was willing to pay Rivers a salary commensurate with what he was making in Boston and had, in fact, already agreed to that aspect of the deal.
"This was about the actual trade," the source said, "and not giving up too many assets" when they still have "plenty of options."
A league source said the Clippers were willing to pay Rivers $7 million per year -- his salary with the Celtics -- over five years.
The Clippers met with Byron Scott for a second time on Tuesday, a Clippers source said, and have a second meeting with Brian Shaw on Wednesday. Both meetings were to include owner Donald Sterling.
Lionel Hollins had a two-day interview in which he met with Sterling last week.
Information from ESPNBoston.com's Chris Forsberg and ESPN The Magazine's Chris Broussard was used in this report.