Paul has an early-termination option in his contract and can become a free agent this summer.
Also, Stein said sources believe the Spurs are considered a lock to at least secure a face-to-face meeting with Paul in free agency.
ESPN.com's Zach Lowe reported in May that there seemed to be mutual interest between CP3 and the Spurs.
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A few days later, Stein reported that the Clippers are taking the threat of San Antonio courting Paul "very seriously."
While Paul could be a strong fit with the Spurs, they would likely need to strip down their roster in order to create enough room to sign the point guard to the $34 million max.
Paul is a nine-time All-Star coming off another strong season, where he averaged 18.1 points, 9.2 assists and 5.0 rebounds per game.
Despite the 32-year-old veteran's continued high level of play, the Clippers have struggled in the playoffs.