Howard and Hennigan sat down face to face in Los Angeles, meeting for the first time since Hennigan became Orlando's GM nearly two weeks ago.
"There's only one team on my list and if I don't get traded there, I'll play the season out and explore my free agency after that," Howard told Yahoo! Sports.
Howard did not specify which team, but Yahoo! Sports said multiple league sources believe that it is the Brooklyn Nets.
Hennigan was noncommittal when Howard told him he wants to be traded to Brooklyn, sources said.
Hennigan did not tell Howard whether he would trade him. His intentions were merely to hear the thoughts of the Magic superstar.
Team spokesman Joel Glass confirmed a meeting between Hennigan and Howard, but declined to discuss any particulars from it.
Howard picked up the option for the final year of his contract with Orlando on March 15. But since then he has grown increasingly disgruntled with the organization, even telling people close to him that he feels the Magic "blackmailed" him into signing the "opt-in" clause. However, some who know Howard say he used the word "blackmailed" incorrectly and simply feels the Magic made promises that have not been kept to get him to sign.
Howard shared his feelings of being blackmailed by the Magic with the NBA Players Association last week, sources said. He -- either himself or through his representatives -- approached the union wondering if he might have a legal complaint against the club.
The goal of such a complaint would be to eliminate his "opt-in," thereby allowing Howard to become a free agent this summer.
Sources said the union is considering whether or not to pursue legal action against the Magic.
Friday was not the first time Howard asked the Magic to trade him. In December, before the lockout-shortened season began, he asked Orlando to deal him to the Nets.
Howard never rescinded his trade offer, even after picking up his option on the day of the trade deadline.
After undergoing surgery on his back in April, Howard asked then-Magic GM Otis Smith to trade him to the Nets, according to sources. Smith said he would seek a trade, but the Magic fired Smith shortly after the season ended.
Information from The Associated Press contributed to this report.