Chris Mannix of Yahoo Sports reported the Spurs are not actively looking to shop their disgruntled star but are open to offers from other teams.
Leonard, 26, has requested a trade from San Antonio after his relationship with the organization and teammates deteriorated over the last year. He missed all but nine games in 2017-18, leading to a distrust between the two parties that has seemingly irreparably damaged the partnership.
Spurs coach Gregg Popovich and Leonard met Tuesday night in Southern California, per ESPN.com's Adrian Wojnarowski and Ramona Shelburne. Their report said Leonard "did not want to sit down with Popovich and has been purposely difficult for the Spurs to reach recently."
Leonard reportedly prefers being sent to Los Angeles, specifically the Lakers. He has one year remaining on his contract and is set to become an unrestricted free agent next summer.
Any team willing to meet the Spurs' demands will almost certainly demand assurances Leonard is committed long-term. The Oklahoma City Thunder rolled the dice with Paul George last summer and could wind up looking silly if George leaves in the offseason while Victor Oladipo soars in Indiana.
With that in mind, a deal is unlikely to get done by Thursday's draft.