According to the Times of India, the Filmfare Award-winning actress and Kashyap held an informal engagement ceremony last month.
The celebrity couple, who met when the filmmaker cast Kalki in Dev D, are said to be getting married at the end of 2011, or early next year.
The French-speaking star will be seen next in the commercial project Zindagi Na Milegi Dobara.
"I can't say too much about the film at the moment," said the Goldsmiths graduate. "We are currently shooting here in Spain. The film stars Abhay Deol, Hrithik Roshan and Farhan Akhtar. It is about their journey: the journey they go through in the film and what each one of them discovers by the end."
The actress has recently completed a UK tour in the stage play Hamlet: The Clown Prince.