It follows the emergence of photographs which appear to show the art collector with his hand around Lawson's neck as the pair sat on the terrace of a restaurant on June 9.
Lawson, 53, the daughter of former chancellor Lord Lawson, was reportedly seen weeping following the episode outside Scott's in Mayfair, central London.
She reportedly left her Chelsea home on Sunday with a suitcase and her 17-year-old son, Bruno.
An onlooker told The Daily Mirror: "Nigella looked on edge but Bruno was very protective of her and keen to look after her."
Saatchi also reportedly left the house on Sunday but returned later refusing to comment.
Lawson's spokesperson told Sky News that "there will be no additional comment today".
Both are said to be regular visitors to the upmarket restaurant in Mount Street, with one report claiming that the couple were there on Saturday, less than a week after the alleged row.
Scotland Yard said that officers from the Community Safety Unit are "carrying out preliminary inquiries" after the photographs appeared in the Sunday People newspaper.
A spokesman said: "Inquiries are in hand to establish the facts in order to assess whether an investigation is necessary."
Police confirmed that they had not received a complaint of assault from Lawson or anyone else.
The Community Safety Unit is designed to tackle hate crime, and the types of incidents they investigate include domestic violence, homophobia and racism.
Lawson wed Saatchi, 70, who made his name in advertising, in 2003.
She has two children, Cosima and Bruno, from her marriage to journalist John Diamond, who died of throat cancer in 2001.
She became a household name in 1998 with her first cookery book, How To Eat.
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