King has made it known that he wants to keep Lopez, and Lopez has repeatedly said that he wants to stay with the only franchise he's played for.
The four-year pro owns career averages of 17.4 points and 7.5 rebounds per contest, but he played in just five games last season thanks to foot and ankle injuries.
King said Lopez visited with doctors on June 18 and has been cleared to resume all basketball-related activity except playing 5-on-5. No timetable for that has been set at this point.
"He's making great progress," King said.
Given that Lopez is a restricted free agent, the Nets will have the right to match any offer.
Lopez is one of several Nets who are set to be free agents on July 1. The team has only four players under contract: shooting guard MarShon Brooks, shooting guard Anthony Morrow, power forward Jordan Williams and center Johan Petro.
Re-signing All-Star point guard Deron Williams remains Brooklyn's biggest priority, but the Nets also have to try to put pieces around him -- assuming he returns.
King was criticized for trading Brooklyn's 2012 first-round pick (No. 6 overall) for combo forward Gerald Wallace, who has since opted out to become an unrestricted free agent himself.
King continued to defend the deal, saying he has no regrets. He made it known that he wants Wallace back -- at the right price -- and thinks it's going to get done.
"We're not gonna just do a deal; if the deal's not right for us, we won't do it," King said. "But I still feel it's a good deal, and at the end of the day we'll figure it out and have him back on the roster."
Power forward Kris Humphries is set to become an unrestricted free agent as well. The Nets, sources said, are interested in soon-to-be unrestricted free agents Ersan Ilyasova and Kevin Garnett, so they may be heading in a different direction.
"We'll be in discussion with (Humphries) and see what numerical number he's looking for," King said. "He also said he wants to play for the Olympic team too."
King said point guard Jordan Farmar has not yet decided on his $4.25 million player option for next season. Farmar has until June 30 to do so.
King said he hopes that unrestricted free agent swingman Gerald Green returns.
"We'd like to have him back," King said.
The Nets have only a late second-round pick (No. 57 overall) in Thursday night's NBA draft but could trade into the first round. The Nets still have the $3 million that is allotted to every NBA team per the rules of the CBA every year to include in a trade, so they could buy a pick.
"If we wanted to, we could get into the first round," King said. "If you asked me right now would we get in the first round, I'd say no, but that could easily change tomorrow."
King says he called new Orlando GM Rob Hennigan to congratulate him on getting the job, but "that's about the extent of the conversations."
The Houston Rockets, sources told ESPN.com, are expected to take a run at Howard as well. King was asked about the Rockets trying to accumulate a bevy of draft picks.
"I don't think it affects us," King said. "Because the fact is, we have their (first-round lottery-protected) pick next year, too. So that kind of impacts it a bit, too."
King disputed a report that the Nets had come to terms with foreign stretch big man Mirza Teletovic, saying no deal has been reached. He declined to discuss the matter further.
Does King feel pressure this offseason, given that his roster is in flux and the team is moving into the $1 billion Barclays Center for 2012-13?
"Not really. And I say that in the sense that we're in good shape capwise," King said. "We could potentially have $35-40 million in cap space, so we can replace our free agents if they choose other places, with other players, so I think that takes a little of the pressure off."
King said the Nets will continue to pursue the same players even if Williams leaves, saying he wants them to play the same style.
"We're building a team," said King, who plans to be active in free agency and the trade market.
What about all the scrutiny he's facing from the fans and the media, clamoring for a contender in Brooklyn in Year 1?
"A good friend that hired me years ago in Philadelphia, (former Sixers owner) Ed Snider, told me, 'If you listen to the fans and media, soon you'll be one,'" King said.
King also said assistant coach Tom Barrise's contract expired and was not renewed. King doesn't have any immediate plans to hire a replacement.
Mike Mazzeo is a regular contributor to ESPNNewYork.com.