League officials said the teams had yet to come to agreement.
Los Angeles put rising star DeAndre Jordan, cash and a first round draft pick on the table in exchange for the veteran coach and power forward, who was prepared to waive his no-trade clause to stick with Rivers.
Officials said the Celtics wanted a second first-round draft pick for the deal.
Even if the two teams can get on the same page, the league might put the kibosh on the trade. A source at the NBA said the league has let them know for "several days" that a trade swapping a coach and a player would violate collective bargaining rules.
"They are chasing the tooth fairy," the source said.
In the meantime, the Clippers brought in Indiana associate head coach Brian Shaw for his second interview.