We've learned the L.A. County Sheriff's Department has one witness they really want a sit-down with ... Mel Gibson.
Sheriff's spokesperson Steve Whitmore tells TMZ, "We would like to speak to Mr. Gibson," adding his department has extended an invitation "but we have not gotten a definitive answer."
As TMZ first reported ... Gibson's lawyers have said they might make their client available at some point in the future.
Mel's lawyers will present their case to the investigating officers next week.
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