Chris Haynes of Yahoo Sports reported Rivers was "a major component in [Kawhi] Leonard joining the Clippers" and the coach will be back with the team next year.
Haynes called any discussions about Rivers losing his job "premature."
Rivers has spent seven seasons as head coach of the Clippers, winning at least 48 games in all but one season, but never advancing to the Western Conference Finals.
Los Angeles had high expectations in the past with rosters that included Chris Paul, Blake Griffin and DeAndre Jordan, but this year's squad was especially hyped after the additions of reigning Finals MVP Kawhi Leonard and six-time All-Star Paul George.
The Clippers were considered a top contender for a championship throughout the year alongside the Los Angeles Lakers and Milwaukee Bucks, and they were still a top choice after building a 3-1 lead over the Denver Nuggets in the Western Conference Semifinals.
However, three straight losses led to the Clippers' elimination, including a 15-point loss in Game 7 on Tuesday night.
It's the second time the squad has blown a 3-1 series lead under Rivers after also losing three straight games against the Houston Rockets in 2015.
Rivers has a 943-681 career regular-season record as a head coach through his time with the Clippers, Boston Celtics and Orlando Magic, ranking 11th in NBA history in wins. However, he has had limited success in the playoffs aside from one championship with the Celtics in 2008.
This year's first-round win over the Dallas Mavericks (in six games) was the first series win for the coach since 2015.
Despite the concerns, the 58-year-old appears likely to return for the 2020-21 season with at least one more chance to lead the Clippers to a title.
With Leonard and George both able to opt out in 2021, however, the coach could have a short leash.