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Mel Gibson will be served with legal papers this week asking him to admit he is the father of a 29-year-old woman from a one-night stand in the back of a car in Australia in 1976.
The News of the World says Gibson, 50, will be required to undergo a DNA test if he denies paternity of Carmel Sloane.
"I'd love it if he recognised us as family," said Carmel, a painter who has a 10-year-old son. "I'm not looking for a meal ticket, I'm happy with my life. I just want to meet the man I've always known was my dad and for him to get to know his grandson."
Carmel's mother, Marilyn, said she met Gibson in Adelaide when he picked her up while she was hitch-hiking to Sydney.
