ORLANDO, Fla. -- Dwight Howard's trade demand from the Orlando Magic is due in part to the organization not granting his requests for specific trades and signings over the last several years, the All-Star center said Sunday night.

Howard requested a trade during several meetings last week and has been given permission by the Magic to have contact with the New Jersey Nets, Los Angeles Lakers and Dallas Mavericks. He went public with the demand Saturday and then followed that up with a strong explanation Sunday, referring to an eroding relationship with Magic general manager Otis Smith.

"I'm pretty sure if you go down the line of teams, every GM has a pretty good relationship with not just the best player but all the players," Howard said. "If you don't have a good relationship with the people you work with, how are you going to get better?"

Orlando is not limiting its Howard trade talks to the three teams, sources close to the situation told ESPN The Magazine's Chris Broussard on Monday. But while the Magic have opened up the talks, they are also holding out hope they can convince Howard, who has vacillated often on his desire to stay or go, to remain in Orlando, a source said.

The Magic would like Andrew Bynum and Pau Gasol from the Lakers, but a source said the Lakers' offer was expected to be Bynum, the trade exceptions acquired in a Lamar Odom trade to Dallas, and two draft picks.

The Nets would attempt to sign Gilbert Arenas if they are able to trade for Howard, a source close to situation told Broussard.

Smith has made several large trades over the last two years in an effort to strengthen the team around Howard before he hit free agency in 2012, trading for Vince Carter before the 2009-10 season and then trading for Gilbert Arenas and Hedo Turkoglu during last season.

Howard said he pushed for other moves that were not made.

Two players Howard has expressed interest in getting within the past year to Smith were Stephen Jackson and Monta Ellis, sources close to the situation told Broussard.

"The stuff that I have asked for, the stuff I felt our team needed to get better, none of it has happened," Howard said. "That's not me being cocky but I want to be involved with the organization. I've been here for a long time, I don't want to sit around."

In an interview with the Orlando Sentinel Sunday night, Smith said he had consulted Howard on trades and other moves.

"When it's your best player, you really do consult your best player on everything? You do," Smith said. "So you consult your best player on free agency. You consult your best players on trades. And that's not uncommon. And I have done that."

Howard declined to be specific about what players he wanted the Magic to acquire but said they weren't all stars or high-salaried players.