Broderick Turner of the Los Angeles Times reported the news relayed by an anonymous executive Thursday.
Paul has an early-termination option in his contract with the Los Angeles Clippers and is expected to become a free agent this offseason.
Turner added that the Clippers have become "nervous" about reports of mutual interest between Paul and the San Antonio Spurs.
To combat the possibility of losing Paul and/or power forward Blake Griffin, the Clippers added Hall of Famer Jerry West to their front office as a consultant Thursday, per Turner.
Paul has spent the past six seasons with the Clips and consistently been one of the premier point guards in the NBA.
During his 12-year career, CP3 has been named to nine All-Star teams, eight All-NBA teams and eight All-Defensive teams.
While his numbers were strong in 2016-17, they did decline slightly to 18.1 points and 9.2 assists per game. He was also limited to 61 games due to injury.
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When healthy, Paul is a game-changer at both ends of the floor, and he would be a massive signing for either Houston or Denver.
The Rockets finished third in the Western Conference last season, and signing Paul could allow them to challenge the Spurs and Golden State Warriors, while also taking some of the burden off James Harden.
Denver missed the playoffs by one game; however, they could make strides with the addition of a superstar like Paul and some consistency at the point guard position in place of Emmanuel Mudiay.
L.A. has a financial leg up on the competition, though, as it can offer him a larger contract than any other team.