This comes only a month after Saatchi was pictured at a Mayfair restaurant covering Lawson's mouth and holding her throat.
Lawson, 53, is said to be the applicant in the case heard by District Judge Aitken.
Together they are reportedly worth an estimated £150m, as well sharing an £11.8m home in Chelsea.
However, it is thought the case will take a matter of minutes, as the pair signed a prenup before marrying in 2003.
Art collector Saatchi is said to be keen to hang on to his multi-million pound collection, and is reportedly negotiating with Nigella's lawyer and cousin Fiona Shackleton, who has previously represented the Royal family and Sir Paul McCartney.
Just weeks ago, 70-year-old Saatchi dropped the bombshell to a UK newspaper that he planned to divorce Nigella, reportedly shocking his estranged wife.
Nigella is currently renting a London home with teen son Bruno, before she flies to LA for a season of filming.