"I like this organization a lot," Williams said, according to the New York Daily News. "I like the direction they're going. They made me and my family feel real comfortable since I've gotten here. I like Coach [Avery] Johnson -- the way he coaches and the way he carries himself. I definitely can see myself staying here."
Williams, who averaged 15.0 points and 12.8 assists in 12 games for the Nets, can opt out of his contract and become an unrestricted free agent after the 2011-12 season. The Nets are slated to move to Brooklyn in 2012-13.
The two-time All-Star said he would be amenable to signing an extension in the offseason.
"I would like to not have the distraction [of my impending free agency] during the season," Williams said, according to the New York Post.
Signing, though, likely would not occur until after a new collective bargaining agreement can be reached between owners and players.
"It's something that's going to be brought up a lot this summer after the collective bargaining agreement handles itself and then we'll look at it," Williams said, according to the Daily News.
Williams had wrist surgery Monday and is expected to rehab for six to eight weeks. The Nets acquired him in a blockbuster trade with the Utah Jazz on Feb. 23.
Williams, who said he felt fine after undergoing the surgery, said that at first he was hesitant about having the procedure.
"I was angry and tried to tell the doctors that I didn't want to have the surgery," Williams said. "The two doctors had me outvoted, two against one. I couldn't do anything about it. They told me that there was no reason to postpone it and if I didn't have it, I would be dealing with the same pain again."
The Nets gave up Derrick Favors, Devin Harris and two first-round picks to get Williams, so they want to lock him up long-term to be the face of the franchise, once the team moves across the Hudson into Barclays Center, its new $1 billion home arena.
Last week, the Nets put up a massive billboard featuring Williams and the slogan "Bound For Brooklyn" in Times Square.
"I think once they made the trade for me, they always talked about me being the face of the franchise towards Brooklyn," Williams said, according to the Daily News. "That's the movement and everything. It's starting to fall in place for the organization. The building is up. It's starting to go up. Ticket sales. Everything is starting to gear towards Brooklyn. So I think they're definitely using me as a big part of that and I like that. Like I said, I like the direction of where things are going."
The Nets wrapped up a 24-58 season Wednesday night with a 97-92 loss to the Bulls in Chicago.
Johnson believes that Williams will be part of the organization for many years to come.
"I feel Deron has totally bought into what we're doing," the Nets coach said. "He's a sincere guy, a man of his word. I have a lot of confidence that he will stay, and I will continue to show him how vitally important he is to the success of our team. I feel good about Deron being in a Nets uniform next season and into the future."
Two of the team's unrestricted free agents also expressed interest in returning. Forward Kris Humphries, who ended up averaging 10 points and 10.4 rebounds per game in his best NBA season, and guard Sasha Vujacic, who averaged 11.4 points in 56 games with the Nets, both said that they hoped to be back.
"I've been saying it a lot lately that I want to be here," said Humphries, who had a meeting scheduled with Johnson and general manager Billy King to discuss his future Thursday. "I like where the team is at, and I want to be a part of it when it all comes together in Brooklyn. I want to keep growing with the franchise."
Vujacic was acquired from the Lakers on Dec. 14.
"My choice would be to come back," said Vujacic, who said he planned to spend a lot of the summer months watching fiancee Maria Sharapova play tennis. "My first goal would be with the Nets. The ownership wants to win, and the Nets have become a global team. It excites me, and this franchise has a very bright future."
Center Brook Lopez, who averaged 20.4 points per game in his third NBA season, feels that the Nets can continue to make strides.
"I'm fairly confident we can continue to improve," Lopez said. "I want Deron to help with the improvement. We can show people a lot next year. It's definitely a better feeling leaving this year compared to last year. I'm much more optimistic that we're going in the right direction."
The Nets opened March with five straight wins, including a pair versus Toronto in London.
"I'm just as excited as I was when I took the job last June," Johnson said. "We knew we had a lot of work to make this a competitive team. I thought it would take two to three years to make it happen. We just weren't good enough from a talent standpoint.
"But our future is bright because of the guys we have."
Mike Mazzeo is a frequent contributor to ESPNNewYork.com. Information from The Associated Press was used in this report.