Formal charges were expected this week. The plea agreement might allow Gibson to avoid jail time.
The Associated Press reported that Gibson will appear in person to enter the plea.
The source, who spoke on the condition of anonymity because the case is ongoing, said if Gibson does plead guilty to the misdemeanor charge, he would face counseling but no jail time. The source said the plea could be announced as early as Wednesday.
"I know from almost 20 years as a criminal defense lawyer that sometimes justice can come for a client at too high a personal price,'' Gibson's attorney, Blair Berk, said in a statement. "That is particularly so for Mel, whose right to due process can only be exercised in this case with an enormous media circus attached."
The statement did not disclose details of the plea agreement.
The two also are involved in a custody dispute over their 1-year-old daughter and an extortion case, which the DA is still considering. In February, sheriff's detectives delivered the results of their extortion investigation to prosecutors.