Bulls No. 1; Clippers 7th

The Chicago Bulls are still coachless. Whoever it is will receive a nice welcoming gift once he signs on.

The Bulls were the winners among the non-winners Tuesday, defying heavy odds to move up eight spots in the NBA’s lottery and will hold the top overall selection in next month’s draft.

The Clippers, who were slotted sixth heading into the lottery, fell to the seventh overall selection after they were bumped by Chicago.

From that position, they probably will evaluate a number of guards, including Indiana’s Eric Gordon, UCLA’s Russell Westbrook and Texas’ D.J. Augustin.

The decision will also hinge on the health of point guard Shaun Livingston, who is still rehabbing after a serious knee injury and expected to begin playing one-on-one soon after spending more than a year sidelined.

“I think we’ll get a good player, no doubt about that,” said Vice President of Basketball Operations Elgin Baylor, who said the team will also look at trade scenarios around draft time.

“I just believe that, from now until draft day, a lot of things can happen. Right now, we think we will make out OK.”

The Bulls have first pick of consensus top prospects: Memphis point guard Derrick Rose, a Chicago native, and Kansas State freshman forward Michael Beasley.

“I don’t think there’s any doubt that those two names are at the top right now,” Bulls General Manager John Paxson said. “We’ll get to know them and really take a long look at what makes the most sense for our basketball team.”

The Bulls, who finished 33-49, held only a 1.7% chance of landing the top spot. They will be followed by the Miami Heat, which held the best odds of landing the top pick.

The draft will be held June 26 in New York. Teams can start bringing in players to evaluate June 3.

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Clippers Coach Mike Dunleavy said Tuesday he expects forward Corey Maggette to use his opt-out clause and become a free agent this off-season.

Dunleavy said he was unsure whether forward Elton Brand would do the same.

He added that he believed both would be interested in re-signing.

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jonathan.abrams@latimes.com