Meanwhile, Clippers star Kawhi Leonard has been ruled out for Thursday's game in Los Angeles. He hasn't played since June 14 because of a sprained right knee.
Paul has been in the league's health and safety protocols since last Wednesday and missed the first two games of the Western Conference finals against the Clippers.
ESPN's Dave McMenamin and Adrian Wojnarowski reported on Tuesday that there was optimism within the Suns organization that Paul could return for Game 3.
Phoenix leads the series 2-0.
Before being sidelined, the 36-year-old Paul averaged 25.5 points on 62.7% shooting while dishing out 41 assists against five turnovers in a four-game sweep of the Denver Nuggets in the second round.