Paul, 28, has just completed his second season with the Clippers and could have become a free agent. ESPN first reported that Paul accepted a five-year, $107 million contract extension.
While Paul posted "I'M IN!!! #ClipperNation" on Twitter, the agreement cannot be finalized until July 10, which is when the NBA moratorium on player signing and trades expires.
Analysts said the recent deal between the Clippers and Boston Celtics to have Doc Rivers become coach of the Clippers likely played a role in Paul's decision to stay in Los Angeles.
Paul has been an all-star selection each of the last six seasons of his eight-season NBA career and was voted the most valuable player of the 2013 All-Star Game. He was drafted by New Orleans in 2005 with the fourth overall pick and was chosen rookie of the year the following season.
The Hornets traded Paul to the Clippers in December 2011.
In 55 NBA regular-season games, Paul averaged 18.6 points and 9.8 assists a game.