The online publication, citing unnamed league sources, said center DeAndre Jordan and two first-round picks would be sent from Los Angeles to the Celtics for in exchange for Garnett and the right to hire Rivers as head coach.
The possible deal is being held up over the Celtics' insistence on including Clippers guard Eric Bledsoe in the package, the sources said.
Under the terms being discussed, Garnett would reportedly waive his no- trade clause to go to the Clippers as long as Rivers were able to accompany him.
The website said Celtics assistant Ty Lue would will likely join the pair in Los Angeles.
Rivers has been Boston's head coach since 2004, leading the team to the 2008 NBA title. The 37-year-old Garnett, meanwhile, has been contemplating retirement.