The court request is part of Gibson's legal team's efforts to peg Grigorieva as the source of leaked audio tapes in which Gibson is heard ranting and raving at the Russian beauty over the telephone.
Grigorieva has claimed the tapes indicate Gibson physically and verbally abused her during their relationship and that she should thus be given sole custody of their daughter, Lucia.
Gibson's legal team insist the tapes were merely being used to set up Gibson, who's been branded "Mad Mel" in the light of several bizarre public meltdowns in which the actor and director is said to have hurled racist and homophobic epithets.
The attorneys previously obtained the seizure of Grigorieva's laptop and iPhone, and now want to inspect her 12-year-old son Sascha's computer to determine whether she used it to distribute the audio recordings, according to celebrity news site Radar Online.
There was no word on whether Sascha is a Mac or Windows user.
Radar Online posted the tapes on its Web site over a period of weeks. In them, an enraged Gibson can be heard threatening Grigorieva, chastising her for wearing revealing clothes, and demanding sex. The tapes sparked a domestic violence investigation by the Los Angeles County Sherriff's Department.
Sascha was born to Grigorieva and James Bond star Timothy Dalton when the two were previously married. He was said to be present during one incident in which Gibson allegedly pulled a gun and threatened to kill Grigorieva.