Spurs GM R.C. Buford would prefer to keep Kawhi Leonard on the team, but will explore all options. (0:22)

SAN ANTONIO -- Spurs general manager R.C. Buford said Thursday night that the franchise's desire is to keep disgruntled All-Star forward Kawhi Leonard in the fold but that the club "will explore all of our options."

Among the issues Leonard has had with the Spurs is his frustration with the team's handling of a quadriceps injury that kept him out of action for all but nine games this past season. Leonard wants to be traded to Los Angeles, preferably to the Lakers, sources have told ESPN.

But Buford expressed the team's willingness to work with Leonard to bridge the gap toward reconciliation.

"Kawhi and his family mean a lot to our organization and to the community," Buford said after the NBA draft. "While none of us would wish we are where we are, we're going to do what we can to build the best relationship we can with him, and we'll explore all of our options. But the first one would be to do what we can to keep Kawhi as a part of our group."

Asked when he'd like to see a resolution between Leonard and the franchise, Buford quipped, "Yesterday." He refuted the notion, however, that time might be working against the Spurs.

"I don't know that timing's a factor in this. ... He's under contract for another year," Buford said. "Our goal is to keep him as a part of our program for a long time."

Leonard has privately told confidants that he no longer wants to play in San Antonio and plans to eventually alert teams considering trades for him that his intention is to sign in Los Angeles when he can become a free agent in 2019, league sources told ESPN's Adrian Wojnarowski.

ESPN's Ramona Shelburne reported the Lakers contacted the Spurs after Leonard's trade desires were reported last week, but the team immediately felt the Spurs didn't plan on engaging in any trade dialogue. No players were discussed during that conversation, and there has been no further dialogue between the teams, according to Wojnarowski.

San Antonio drafted Miami shooting guard Lonnie Walker IV with the No. 18 pick Thursday and used its second-round pick to select USC's Chimezie Metu. While it was expected the Spurs would field plenty of potential trade offers for Leonard throughout the draft, the team finished the day with Leonard still on the roster and hopes to keep it that way.

Spurs coach Gregg Popovich traveled to Southern California on Tuesday and met with Leonard ahead of the draft to discuss issues that have shaken the franchise's relationship with the All-NBA forward, league sources told ESPN.

Buford declined to say whether Leonard had made a formal request with the team for a trade, and according to sources, the Spurs were unaware of Leonard's desire to be moved when his intentions became public.

Leonard had expressed to confidants that he did not want to sit down with Popovich before their Tuesday meeting. Leonard and his representatives have been miffed over what they believe was the Spurs' mishandling of his quadriceps injury, and they're also upset over public comments from teammate Tony Parker and Popovich that they felt were not supportive of Leonard, league sources said.

Buford acknowledged that perhaps mistakes have been made on both sides, saying, "All of us would wish that things would have gone differently at times."

A two-time first-team All-NBA player, Leonard is eligible to sign a five-year, $219 million super-maximum contract with the Spurs this summer. The Spurs' official priority had been to try to talk with Leonard to work through the issues, league sources said, and the plan is for the sides to continue to talk beyond Tuesday's initial meeting.

That has been communicated to teams seeking trade talks, but the Spurs have also encouraged some rival team executives calling about Leonard to present an offer if they choose, sources said. The Spurs have been reluctant to provide guidance to teams on the players, or packages, that would interest them in trades, sources said.