Mel – who split with Oksana last year, amid claims he had threatened to bury her in his rose garden – has filed a request with a court to request additional overnight stays with the youngster, reports website TMZ.
However, nothing will be decided until a hearing in September.
'The Beaver' actor has previously confessed he has found his life "hard to bear" at times, but believes everyone goes through tough times at some point in their lives.
He said: "We all go through things that are hard to bear at some point or other, and we have to get through it. About life, oh boy. You don't want to hear about my three-ring circus."
Earlier this year, Oksana – who also has 14-year-old son Alexander with British actor Timothy Dalton – dropped a domestic violence claim against Mel.
Mel Gibson is reportedly dating a 25-year-old fetish model
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Oksana Grigorieva has asked a California judge to disqualify Mel Gibson's lawyers in her custody case with the actor