Leonard did not want the meeting and has been making himself hard to reach for the Spurs on objective, according to ESPN's report.
ESPN initially reported that Popovich was flying to California to meet with Leonard before Thursday's (Friday, PHL time) Draft before amending its report to indicate the meeting had taken place on Tuesday (Wednesday, PHL time).
The Spurs star forward - who can become an unrestricted free agent in 2019 - is looking for a trade to Los Angeles, preferably the Lakers, league sources said.
Reports are conflicting as to whether Popovich and Leonard actually met.
Leonard is angry over how the Spurs handled his quad rehab and is irate with public comments made by Tony Parker.
The Spurs are unlikely to be motivated to facilitate a deal to the Lakers, league sources said.
Various reports over the last few months indicated the sides disagreed about the nature of Leonard's injury, how to treat it and how soon he would be able to return to the floor.
Leonard, a two-time Defensive Player of the Year, has played all seven of his National Basketball Association seasons with the Spurs.
Wojnarowski reported that the Spurs haven't given suitors guidance on what they'd be seeking for Leonard in a trade. However, one thing to consider with Leonard is the fact that he's eligible for a five-year, $219-million super-max contract extension with San Antonio, so there's a lot of money he could be leaving on the table if he does indeed force his way out.