New L.A. D.A. Nathan Hochman Says Menendez Brothers Case Is High Priority

Incoming Los Angeles County District Attorney Nathan Hochman says one of his first orders of business is tackling Erik and Lyle Melendez's bid for freedom ... and the clock's ticking.

Hochman, who just defeated incumbent George Gascón at the ballot box, tells TMZ ... if the Menendez brothers' resentencing case lands on his desk on his first day as D.A., on December 2, he will hit the ground running, poring over documents and talking to all parties involved.

While Gascon has recommended resentencing, Hochman says he's got to review the case and the law before coming to a decision ... but time is of the essence because the resentencing hearing is set for Dec. 11 ... giving Hochman a little over a week to work with.

Ultimately, a judge will decide if Erik and Lyle will become free men ... either by getting the ball rolling on a possible release on parole, or by changing their conviction and setting them free ASAP based on time served ... the latter of which is supported by the Menendez brothers' attorney, Mark Geragos.

Hochman sounds pretty interested in the case, but he says he's not going to make it some big political stunt like Gascón ... ripping the outgoing D.A. for sitting on the case until he was so far down in the polls he thought it might help him win reelection.

California Governor Gavin Newsom could also step in at any time and pardon Erik and Lyle or commute their sentences ... so there's a chance Hochman doesn't even have to deal with this by the time he takes office.

But, as Hochman tells us ... the case will get his full attention if it lands on his desk when he starts his new job.