James Ford Seale is seeking to overturn his conviction for kidnapping two black men who were killed in rural Mississippi in 1964.
Court officials say a decision could be announced shortly after a Sept. 27 conference on the case.
Seale is now 75-years-old.
He was convicted in 2007 of two counts of kidnapping and one count of conspiracy to commit kidnapping.
For the convictions Seale was given three life sentences.
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