View Photo Gallery: Gene Wang predicts the first 15 picks of the 2012 NBA Draft.

The Houston Rockets have acquired their third top-20 pick in Thursday’s NBA draft, creating the kind of stockpile that fuels speculation they’ll make a run at a deal for Orlando Magic center Dwight Howard.

The Rockets traded forward Chase Budinger and the rights to Israeli player Lior Eliyahu to the Minnesota Timberwolves for the 18th overall pick. Houston already has the 14th and 16th picks.

Howard, who can become a free agent next summer and was the subject of trade rumors all year, is believed to want to be traded to Brooklyn, Dallas or Los Angeles, but the Rockets seem to think they can convince him to re-sign before hitting the free-agent market. The Magic had been talking with Orlando until just before the March 15 tradeline, but were seeking more than a 14th pick.

Howard, who had back surgery in May, could have become a free agent this summer but did not. Nor did he indicate to the Magic that he is interested in returning after a bizarre season in Orlando.

Still Rob Hennigan, the Magic’s new general manager, said he intends to “reach out to Howard” soon and discuss his vision for the future.

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