The former couple share custody of their six-year-old daughter Lucia and the 46-year-old singer/songwriter is mounting a legal battle to increase the "Mad Max" actor's financial liability to more than USD 1 million per year, according to TMZ.
Oksana currently receives USD 20,000 each month as part of a total settlement of USD 750,000 and a house in Sherman Oaks, California, where she lives with the little girl.
When Lucia turns 18 the house will be sold and the proceeds turned into a trust fund for her.
The case is about to go to trial, with the musician - who hails from Russia - claiming she needs to support a lifestyle of vacations, travel, lodging and other items.
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The couple have rarely seen eye to eye since the little girl was born and previously had restraining orders out against each other.
They also locked horns in July 2010 when Gibson, 60, was identified as a possible suspect in a domestic violence case which Oksana later dropped.
"The Passion of the Christ" director has seven other children with ex-wife Robyn.