Linda Evangelista has petitioned a Manhattan court for $46,000 a month in child support.
The supermodel has petitioned a family court in Manhattan, New York, to award the huge sum for the care of five-year-old Augustin, who was conceived during the beauty's relationship with the French billionaire.
Despite Pinault's vast wealth it is unlikely Evangelista will get the maintenance settlement she is demanding.
Manhattan divorce lawyer Raoul Felder told the New York Daily News newspaper: ''She's in for a big surprise. I wouldn't be counting the money yet ... most of the time, there are formulas for this. There's no windfall in child support.''
Pinault - who is married to actress Salma Hayek - is the CEO of PPR, the French multinational holding company which part owns YVES SAINT LAURENT and Gucci and was started by his father Francois Pinault.
Pinault has previously insisted Augustin is ''totally integrated'' into his family, despite claims made by Evangelista he has paid nothing to support his son since he was born in October 2006.
He said: ''At every possible opportunity he [Augustin] has participated in my family life whether in France or the United States. He is totally integrated within my family.''
Pinault has three other children, including four-year-old Valentina with Salma.